35:
6246:
An estimate for something that is often but not always correct, such as virtual genus, virtual dimension, and so on. If some number is given by the dimension of a space of sections of some sheaf, the corresponding virtual number is sometimes given by the corresponding Euler characteristic, and equal
1836:
often has dimension at least 3, because when it has dimension 2 these are more or less the same as covariants. The degree and class of a contravariant are its degrees in the two types of variable. Contravariants generalize invariants and are special cases of concomitants, and are in some sense dual
393:
Definitions in classical algebraic geometry were often somewhat vague, and it is futile to try to find the precise meaning of some of the older terms because many of them never had a precise meaning. In practice this did not matter much when the terms were only used to describe particular examples,
1351:
A plane conic passing through the circular points at infinity. For real projective geometry this is much the same as a circle in the usual sense, but for complex projective geometry it is different: for example, circles have underlying topological spaces given by a 2-sphere rather than a 1-sphere.
327:
On the other hand, while most of the material treated in the book exists in classical treatises in algebraic geometry, their somewhat archaic terminology and what is by now completely forgotten background knowledge makes these books useful to but a handful of experts in the classical literature.
412:
Several terms, such as "Abelian group", "complete", "complex", "flat", "harmonic", "homology", "monoid", "normal", "pole", "regular", now have meanings that are unrelated to their original meanings. Other terms, such as "circle", have their meanings tacitly changed to work in complex projective
3122:
or
Hessian duad of three points on a projective line is the pair of points fixed by the projective transformations of order 3 permuting the 3 points. More generally the Hessian pair is also defined in a similar way for triples of points of a rational curve, or triples of elements of a pencil.
2832:
Most particularly we refer to the recurrent use of such adjectives as `general' or `generic', or such phrases as `in general', whose meaning, wherever they are used, depends always on the context and is invariably assumed to be capable of unambiguous interpretation by the reader.
378:...we refer to a certain degree of informality of language, sacrificing precision to brevity, ..., and which has long characterized most geometrical writing. ... depends always on the context and is invariably assumed to be capable of unambiguous interpretation by the reader.
111:. Much of the classical terminology, mainly based on case study, was simply abandoned, with the result that books and papers written before this time can be hard to read. This article lists some of this classical terminology, and describes some of the changes in conventions.
1853:
An isomorphism from a projective space to the dual of a projective space, often to the dual of itself. A correlation on the projective space of a vector space is essentially the same as a nonsingular bilinear form on the vector space, up to multiplication by constants.
3951:
An algebraic manifold is a cycle of projective space, in other words a formal linear combination of irreducible subvarieties. Algebraic manifolds may have singularities, so their underlying topological spaces need not be manifolds in the sense of differential topology.
342:
The change in terminology from around 1948 to 1960 is not the only difficulty in understanding classical algebraic geometry. There was also a lot of background knowledge and assumptions, much of which has now changed. This section lists some of these changes.
2967:
is an archaic term for an effective divisor on a curve. This usage is particularly confusing, because some such divisors are called normal, with the result that there are "normal sub-groups" having nothing to do with the normal subgroups of group theory.
4565:
An isomorphism between two projective lines (or ranges) of projective space such that the lines joining each point of one line to the corresponding point of the other line all pass through a fixed point, called the center of the perspectivity or the
4732:
A correlation given by a symmetrical matrix, or a correlation of period 2. A polarity of the projective space of a vector space is essentially a non-degenerate symmetric bilinear form, up to multiplication by scalars. See also null-polarity.
806:
A special line or linear subspace associated with some family of geometric objects. For example, a special linear complex in 4-dimensional space consists of all lines meeting a given plane, that is called the axial plane of the complex.
4083:
The multiplicity of a point on a hypersurface is the degree of the first non-vanishing coefficient of the Taylor series at the point. More generally one can define the multiplicity of any point of a variety as the multiplicity of its
3404:
An inflection is a point where the curvature vanishes, or in other words where the tangent line meets with order at least 3. Differential geometry uses the slightly stricter condition that the curvature changes sign at the point. See
4252:
A correlation given by a skew symmetric matrix. A null-polarity of the projective space of a vector space is essentially a non-degenerate skew-symmetric bilinear form, up to multiplication by scalars. See also polarity.
350:
In classical algebraic geometry, all curves, surfaces, varieties, and so on came with fixed embeddings into projective space, whereas in scheme theory they are more often considered as abstract varieties. For example, a
5802:
The tangential equation of a plane curve is an equation giving the condition for a line to be tangent to the curve. In other words it is the equation of the dual curve. It is not the equation of a tangent to a
1965:
often has dimension 2. The degree and order of a covariant are its degrees in the two types of variable. Covariants generalize invariants and are special cases of concomitants, and are in some sense dual to
6070:
A set of 5 partitions of a 6-element set into three pairs, such that no two elements of the total have a pair in common. For example, {(12)(36)(45), (13)(24)(56), (14)(26)(35), (15)(23)(46), (16)(25)(34)}
1315:
2. A characteristic exponent is an exponent of a power series with non-negative coefficient, that is not divisible by the highest common factor of preceding exponents with non-zero coefficients.
5325:
1. If a line meets a cubic curve in 3 points, the residual intersections of the tangents of these points with the cubic all lie on a line, called the satellite line of the original line. See
408:
Readers were often assumed to know classical (or synthetic) projective geometry, and in particular to have a thorough knowledge of conics, and authors would use terminology from this area without further
2761:
1. The fundamental set or fundamental locus of a birational correspondence appears to mean (roughly) either the set of points where it is not a bijection or the set of points where it is not
5542:
Intersecting in a set that is either empty or of the "expected" dimension. For example skew lines in projective 3-space do not intersect, while skew planes in projective 4-space intersect in a point.
749:
An apparent singularity is a singularity of a projection of a variety into a hyperplane. They are so called because they appear to be singularities to an observer at the point being projected from. (
1628:
A (mixed) concomitant is an invariant homogeneous polynomial in the coefficients of a form, a covariant variable, and a contravariant variable. In other words it is a (tri)homogeneous polynomial on
1664:
often has dimension 2. The degree, class, and order of a concomitant are its degrees in the three types of variable. Concomitants are generalizations of covariants, contravariants, and invariants.
3240:
2. A collineation fixing all lines through a point (the center) and all points through a line (the axis) not containing the center. See elation. This terminology was introduced by Lie.
1780:
Infinitesimally near. For example, a tangent line to a curve is a line through two consecutive points of the curve, and a focal point is the intersection of the normals of two consecutive points.
1323:
3. The characteristic series of a linear system of divisors on a surface is the linear system of 0-cycles on one of the divisors given by its intersections with the other divisors.
7027:"On a Theory of the Syzygetic Relations of Two Rational Integral Functions, Comprising an Application to the Theory of Sturm's Functions, and That of the Greatest Algebraical Common Measure"
413:
space; for example, a circle in complex algebraic geometry is a conic passing through the circular points at infinity and has underlying topological space a 2-sphere rather than a 1-sphere.
2239:
2. A differential of the second kind is a meromorphic 1-form such that the residues of all poles are 0. Sometimes it is only allowd to have one pole that must be of order 2.
365:
Until circa 1950, many of the proofs in classical algebraic geometry were incomplete (or occasionally just wrong). In particular authors often did not bother to check degenerate cases.
5007:
A quadro-cubic or quadro-quartic transformation is a
Cremona transformation such that the homaloids of the transformation have degree 2 and those of its inverse have degree 3 or 4. (
3790:
3990:
1. A variety whose points (or sometimes hyperplane sections) correspond to elements of some family. Similar to what is now called a parameter space or moduli space.
4841:
A postulated object (point, line, and so on) is an object in some larger space. For example, a point at infinity of projective space is a postulated point of affine space. (
1578:, a family of lines of codimension 1 in the family of all lines in some projective space, in particular a 3-dimensional family of lines in 3-dimensional projective space. (
118:) translates many of the classical terms in algebraic geometry into scheme-theoretic terminology. Other books defining some of the classical terminology include Baker (
4786:) to the projective line. The degree of the map is called the gonality of the curve. When the degree is 1, 2, or 3 the curve is called rational, hyperelliptic, or trigonal.
533:
467:
2242:
3. A differential of the third kind is sometimes a meromorphic 1-form such that all poles are simple (order 1). Sometimes it is only allowed to have 2 poles.
585:
1. A fixed choice of something in projective space, used to construct some other geometry from projective geometry. For example, choosing a plane, called the
1680:
1. The union of the lines joining an algebraic set with a linear algebraic set. Called a point-cone, line-cone, ... if the linear set is a point, line, ...(
3165:
1. A homaloidal linear system of divisors is a linear system of grade 1, such as the image of the linear system of hyperplanes of projective space under a
7031:
6677:
6634:
3471:(Noun) A polynomial in the coefficients of a homogeneous form, invariant under some group of linear transformations. See also covariant, contravariant, concomitant.
3203:
2. A homographic transformation is an automorphism of projective space over a field, in other words an element of the projective general linear group. (
1969:
2. The variety defined by a covariant. In particular the curve defined by the
Hessian or Steinerian covariants of a curve are called covariant curves. (
6514:
Principles of geometry. Volume 4. Higher geometry. Being illustrations of the utility of the consideration of higher space, especially of four and five dimensions
2521:
In intersection theory, a positive-dimensional variety sometimes behaves formally as if it were a finite number of points; this number is called its equivalence.
4766:
The poloconic (also called conic polar) of a line in the plane with respect to a cubic curve is the locus of points whose first polar is tangent to the line. (
4694:
2. The polar conic is the zero set of the quadratic form associated to a polarity, or equivalently the set of self-conjugate points of the polarity.
6294:
A point on a curve where the dimension of the space of rational functions whose only singularity is a pole of some order at the point is higher than normal.
4645:
is one of the 15 lines containing 4 of the 20 Steiner points associated to 6 points on a conic. The Plücker lines meet in threes at the 60 Kirkman points. (
1092:
Both circumscribed and inscribed, or in other words having vertices that lie on a curve and sides that are tangent to the curve, as in biscribed triangle. (
793:
1. An associated curve is the image of a projective curve in a
Grassmannian, given by taking the tangent lines, or osculating planes, and so on.
2927:
generic divisors. In particular the grade of a linear series of divisors on a curve is now called the degree and is the number of points in each divisor (
347:
In classical algebraic geometry, adjectives were often used as nouns: for example, "quartic" could also be short for "quartic curve" or "quartic surface".
5456:
2. A self-conjugate (or self-polar) triangle (or triad) is a triangle such that each vertex corresponds to the opposite edge under a polarity.
1084:
2. Two varieties are biregular if there is a biregular map from one to the other, in other words if they are isomorphic as abstract varieties.
4976:
1. A Cremona transformation of degree 2. A standard quadratic transformation is one similar to the map taking each coordinate to its inverse.
4853:
The postulation of a variety for some family is the number of independent conditions needed to force an elements of the family to contain the variety. (
4805:
2. An arrangement of geometrical figures (such as lines or circles) that are inscribed in one curve and circumscribed around another, as in
358:
Varieties were often considered only up to birational isomorphism, whereas in scheme theory they are usually considered up to biregular isomorphism. (
368:
Words (such as azygetic or bifid) were sometimes formed from Latin or Greek roots without further explanation, assuming that readers would use their
4642:
3696:
1491:
1. A coincidence quadric is a quadric associated to a correlation, given by the locus of points lying in the corresponding hyperplane. (
1563:
91:
The terminology of algebraic geometry changed drastically during the twentieth century, with the introduction of the general methods, initiated by
17:
6346:
5313:
The Salmon conic of a pair of plane conics is the locus of points such that the pairs of tangents to the two conics are harmonically conjugate. (
2758:
This term seem to be ambiguous and poorly defined: Zariski states: "I can find no clear-cut definition of a fundamental curve in the literature".
1699:
is a finite set of points and lines (and sometimes planes), generally with equal numbers of points per line and equal numbers of lines per point.
5857:
A geometric configuration consisting of 4 points and the 6 lines joining pairs. This is similar to the lines and infinite edges of a polyhedral
4130:
2. A harmonic net is a set of points on a line containing the harmonic conjugate of any point with respect to any other two points. (
954:
is a permutation of the 28 bitangents of a quartic curve depending on one of the 35 decompositions of 8 symbols into two sets of 4 symbols. See
6356:
5974:
A set of 3 planes A Steiner trihedral is a set of three tritangent planes of a cubic surface whose intersection point is not on the surface. (
5027:
A Quarto-quartic transformation is a
Cremona transformation such that the homaloids of the transformation and its inverse all have degree 4. (
3115:
3. The
Hessian point is a point associated to three lines tangent to a conic, whose construction is dual to that of a Hessian line.
6616:
3448:
An integral is (more or less) what is now called a closed differential form, or sometimes the result of integrating such a form..
616:
An accidental (or improper) double point of a surface in 4-dimensional projective space is a double point with two distinct tangent planes. (
5121:
2. The rank of a projective surface is the rank of a curve given by the intersection of the surface with a generic hyperplane. (
5114:
1. The rank of a projective curve is the number of tangents to the curve meeting a generic linear subspace of codimension 2. (
2765:
2. A fundamental point, curve, or variety is a point, curve, or variety in the fundamental set of a birational correspondence.
2024:
A cubo-cubic transformation is a
Cremona transformation such that the homaloids of the transformation and its inverse all have degree 3.
5732:
3. A linear relation between generators of a module, or more generally an element of the kernel of a homomorphism of modules.
589:, of projective space can be used to make its complement into a copy of affine space. Choosing a suitable conic or polarity, called the
6366:
6102:
A point of undulation of a curve is where the tangent meets the curve to fourth order; also called a hyperflex. See inflection point. (
1498:
2. A fixed point of a correspondence, in other words a point of a variety corresponding to itself under a correspondence. (
4813:. There seems to be some confusion about whether "porism" refers to the geometrical configuration or to the statement of the result.
2672:
1. A focal point, line, plane, ... is the intersection of several consecutive elements of a family of linear subspaces. (
5453:
1. Incident with its image under a polarity. In particular the self-conjugate points of a polarity form the polar conic.
4598:
is a singular point of a surface, where the two tangent planes of a point on a double curve coincide in a double plane, called the
785:
One of the 288 sets of 7 of the 28 bitangents of a quartic curve corresponding to the 7 odd theta characteristics of a normal set.
355:
was not just a copy of the projective plane, but a copy of the projective plane together with an embedding into projective 5-space.
2166:
1. The number of intersection points of a projective variety with a generic linear subspace of complementary dimension
1753:
3. A conjugate line is a line containing the point corresponding to another line under a polarity (or plane conic). (
6376:
5930:
A line meeting several other lines. For example, 4 generic lines in projective 3-space have 2 transversals meeting all of them.
5550:
A 3-dimensional linear subspace of projective space, or in other words the 3-dimensional analogue of a point, line, or plane. (
4353:
A double point of a plane curve that is also a point of osculation; in other words the two branches meet to order at least 3. (
4173:
6280:
A quartic surface in projective space given by the locus of the vertex of a cone passing through 6 points in general position.
7101:
7005:
6931:
6903:
6880:
6849:
6810:
6772:
6739:
6590:
6558:
6526:
6494:
6462:
6422:
2571:
on a surface is one that corresponds to a simple point on another surface under a birational correspondence. It is called an
2275:
6030:
Meeting something in 3 tangent points, such as a tritangent conic to a cubic curve or a tritangent plane of a cubic surface.
6793:
1566:
in the plane is a (possibly degenerate) conic, together with a pair of (possibly equal) points on it if it is a double line
96:
5208:
Two ranges (labeled sets) of points on a line are called related if there is a projectivity taking one range to the other.
1438:
1. The class of a plane curve is the number of proper tangents passing through a generic point of the plane. (
1445:
2. The class of a space curve is the number of osculating planes passing through a generic point of space. (
7137:
5690:
A partition of a set of 6 elements into 3 pairs, or an element of the symmetric group on 6 points of cycle shape 222. (
5459:
3. A self-conjugate tetrad is a set of 4 points such that the pole of each side lies on the opposite side. (
4233:
3. A normal intersection is an intersection with the "expected" codimension (given a sum of codimensions). (
2114:
of a plane curve is an approximation to its genus, equal to the genus when all singular points are ordinary, given by (
6083:
The type of a projective surface is the number of tangent planes meeting a generic linear subspace of codimension 4. (
4921:
An isomorphism between two projective lines (or ranges). A projectivity is a product of at most three perspectivities.
1933:,... that is invariant under some group of linear transformations. In other words it is a bihomogeneous polynomial on
1804:,... that is invariant under some group of linear transformations. In other words it is a bihomogeneous polynomial on
6153:
1. A correspondence is called unirational if it is generically injective, in other words a rational map. (
5019:
A homogeneous polynomial in several variables, now usually called a form. Not to be confused with quartic or quadric.
1308:
of a curve are the order, class, number of nodes, number of bitangents, number of cusps, and number of inflections. (
78:
56:
2931:, p.345), and the grade of a net of curves on a surface is the number of free intersections of two generic curves. (
1750:
2. A conjugate point is a point lying on the hyperplane corresponding to another point under a polarity.
1715:
A family of lines in projective space such that there are a nonzero finite number of lines through a generic point (
49:
3034:
is a set of points on a line containing the harmonic conjugate of any point with respect to any other two points. (
1456:
dimensional projective space is the number of tangent planes meeting a generic codimension 2 subspace in a line. (
5368:
with an embedding into projective space so that the lines of the ruled surface are also lines of projective space.
4059:
A Cremona transformation of projective space generated by a family of monoids with the same point of multiplicity
2679:
2. A focal curve, surface and so on is the locus of the focal points of a family of linear subspaces. (
6351:
3457:
3. An integral of the third kind is a meromorphic closed differential form whose poles are all simple.
2270:
A straight line, or more generally a projective space, associated with some geometric configuration, such as the
1479:
A family of plane circles all passing through the same two points (other than the circular points at infinity). (
5729:
2. An algebraic relation between generators of a ring, especially a ring of invariants or covariants.
4873:
to be the product of the distances from the point to the intersections with a circle through it, divided by the
6756:
6341:
4308:
2994:
1. Two pairs of points on a line are harmonic if their cross ratio is –1. The 4 points are called a
2855:
2. A generic point is one having coordinates that are algebraically independent over the base field.
2107:
1. The deficiency of a linear system is its codimension in the corresponding complete linear system.
1534:
1. A linear series of divisors is called complete if it is not contained in a larger linear series.(
5722:
1. A point is in syzygy with some other points if it is in the linear subspace generated by them. (
1300:
1. An integer associated with a projective variety, such as its degree, rank, order, class, type. (
5794:
is a cone defined by the non-zero terms of smallest degree in the Taylor series at a point of a hypersurface.
3727:
2349:
601:, in the absolute plane provides the means to put a metric on affine space so that it becomes a metric space.
5586:
A collection of lines (and sometimes planes and so on) with a common point, called the center of the star. (
416:
Sometimes capital letters are tacitly understood to stand for points, and small letters for lines or curves.
7132:
6361:
5710:
Paired. Opposite of azygetic, meaning unpaired. Example: syzygetic triad, syzygetic tetrad, syzygetic set,
2271:
2254:
of a conic is the locus of points where two orthogonal tangent lines to the conic meet. More generally the
6114:
Having only one branch at a point. For example, a cusp of a plane curve is unibranch, while a node is not.
4017:
A function of algebraic varieties depending only on the isomorphism type; in other words, a function on a
3978:
Two tetrads such that the plane containing any three points of one tetrad contains a point of the other. (
3023:
of an inflection point of a cubic curve is the component of the polar conic other than the tangent line. (
7127:
6328:
4877:
th power of the diameter. He showed that this is independent of the choice of circle through the point. (
4420:
3009:-invariant 1728, given by a double cover of the projective line branched at 4 points with cross ratio –1.
4442:
2. A parallel curve is the envelope of a circle of fixed radius moving along another curve. (
3524:
3454:
2. An integral of the second kind is a meromorphic closed differential form with no residues.
1261:
3. The Cayley lines or Cayley–Salmon lines are the 20 lines passing through 3 Kirkman points.
819:
Unpaired. Opposite of syzygetic, meaning paired. Example: azygetic triad, azygetic tetrad, azygetic set.
6841:
6802:
6582:
6550:
6518:
6486:
6446:
6406:
3332:
Same as point of undulation: a point of a curve where the tangent line has contact of order at least 4.
394:
as in these cases their meaning was usually clear: for example, it was obvious what the 16 tropes of a
3684:
Horn-like. A keratoid cusp is one whose two branches curve in opposite direction; see ramphoid cusp.
668:
are required to be ordinary, and if theis condition is not satisfied the term "sub-adjoint" is used. (
6371:
5168:
4595:
4226:
2. Orthogonal to the tangent space, such as a line orthogonal to the tangent space or the
3925:
3714:
3536:
2614:
1. (Noun) A linear subspace of projective space, such as a point, line, plane, hyperplane.
2557:
1. Corresponding to something of lower dimension under a birational correspondence, as in
2359:
of a plane curve is the set of its tangent lines, considered as a curve in the dual projective plane.
719:
is a large variety containing all the points, curves, divisors, and so on that one is interested in.
5224:
The residual intersection of two varieties consists of the "non-obvious" part of their intersection.
5102:
Beak-like. A ramphoid cusp is one whose two branches curve in the same direction; see keratoid cusp.
4104:
4063:–1. More generally a blow-up along a subvariety, called the center of the monoidal transformation. (
6578:
Principles of geometry. Volume 6. Introduction to the theory of algebraic surfaces and higher loci.
5562:
An effective divisor whose first cohomology group (of the associated invertible sheaf) is non-zero.
4979:
2. A monomial transformation with center a point, or in other words a blowup at a point.
4148:
The convex hull of the points with coordinates given by the exponents of the terms of a polynomial.
1404:
1392:
500:
434:
43:
6482:
Principles of geometry. Volume 3. Solid geometry. Quadrics, cubic curves in space, cubic surfaces.
4115:
Two components (circuits) of a real algebraic curve are said to nest if one is inside the other. (
3215:
1. An isomorphism between projective spaces induced by an isomorphism of vector spaces.
2494:
An equiaffinity is an equiaffine transformation, meaning an affine transformation preserving area.
6866:
6731:
4906:
4318:
2. The order of a covariant or concomitant: its degree in the contravariant variables.
1696:
5702:
A family of algebraic sets in projective space; for example, a line system is a family of lines.
5433:
is the product of two projective spaces, or an embedding of this into a larger projective space.
4833:
imply that if there is one way to arrange lines or circles then there are infinitely many ways.
4311:: the number of intersection points with a generic linear subspace of complementary dimension. (
3974:
3243:
3. An automorphism of projective space with a hyperplane of fixed points (called the
761:
Orthogonal under the polar pairing between the symmetric algebra of a vector space and its dual.
7022:
6611:
5831:
5244:
5047:
Degree 4, especially a degree 4 projective variety. Not to be confused with quantic or quadric.
4987:
Degree 2, especially a degree 2 projective variety. Not to be confused with quantic or quartic.
4954:
4322:
3539:
is the dimension of the space of holomorphic 1-forms on a non-singular projective surface; see
3512:
3166:
3154:
2446:
An embedded variety is one contained in a larger variety, sometimes called the ambient variety.
1982:
1609:
1556:
1062:
1. Two varieties are birational if they are isomorphic off lower-dimensional subsets
846:
108:
60:
2329:
6989:
6953:
5987:
4546:
4220:
2178:
1215:
1023:
A double point of a surface whose tangent cone consists of two different planes. See unode. (
905:
893:
A pair of integers giving the degrees of a bihomogeneous polynomial in two sets of variables
7111:
7015:
6913:
6859:
6782:
6764:
6749:
6600:
6568:
6536:
6504:
6472:
6432:
6138:
5766:
A singularity of a plane curve where a tacnode and a cusp are combined at the same point. (
5534:
Special in some way, including but not limited to the current sense of having a singularity
5200:
One of the two pencils of lines on a product of two projective planes or a quadric surface.
4826:
4806:
4799:
4522:
4416:
4409:
4127:
1. A 2-dimensional linear system. See "pencil" and "web". See also
Laguerre net.
1411:
5966:
A trigonal curve is one with a degree three map to the projective line. See hyperelliptic.
3463:
5. A double integral is a closed 2-form, or the result of integrating a 2-form.
3460:
4. A simple integral is a closed 1-form, or the result of integrating a 1-form.
2852:
1. Not having some special properties, which are usually not stated explicitly.
1476:
A pencil of circles is called coaxal if their centers all lie on a line (called the axis).
8:
6442:
Principles of geometry. Volume 2. Plane geometry, Conics, circles, non-Euclidean geometry
6309:
6039:
5911:
5870:
4830:
4810:
4471:
3800:
3321:
3127:
2976:
2562:
2226:
2219:
2212:
2201:
1. (Noun) A 1-dimensional family of planes in 3-dimensional projective space (
1549:
1368:
depending on whether it has an even or odd number of intersections with a generic line. (
6893:
6180:
A double point of a surface whose tangent cone consists of one double plane. See binode.
5861:, but in algebraic geometry one sometimes does not include the faces of the tetrahedron.
5510:
A simple point of a variety is a non-singular point. More generally a simple subvariety
5083:
The quotient ring of a point (or more generally a subvariety) is what is now called its
3088:, of a conic, containing the three points given by the intersections of the tangents at
2870:
1. The dimension of the space of sections of the canonical bundle, as in the
1731:
is a degree 2 curve. Short for "conic section", the intersection of a cone with a plane.
773:
of a variety is a variation of the Euler characteristic of the trivial line bundle; see
7066:
7058:
6978:
6833:
6710:
6702:
6661:
6019:
5186:
5175:
4697:
3. (Noun) The first polar, second polar, and so on are varieties of degrees
3516:
3480:
2743:
2431:
2045:
1254:
is a set of 8 points in projective space given by the intersection of three quadrics. (
6921:
6172:
A point in the intersection of the diagonal and a correspondence from a set to itself.
3451:
1. An integral of the first kind is a holomorphic closed differential form.
2177:
The
Desargues figure or configuration is a configuration of 10 lines and 10 points in
1463:
4. The degree of a contravariant or concomitant in the covariant variables.
487:
7097:
7070:
7050:
7001:
6982:
6970:
6927:
6899:
6876:
6845:
6806:
6768:
6735:
6714:
6694:
6653:
6586:
6576:
6554:
6544:
6522:
6512:
6490:
6480:
6458:
6440:
6418:
6400:
6290:
5947:
4583:
4292:
3520:
2723:
2558:
2502:
1. Four points whose cross ratio (or anharmonic ratio) is a cube root of 1
2190:
605:
562:
104:
4632:
3896:
A line in projective space; in other words a subvariety of degree 1 and dimension 1.
1395:
is a curve passing through the two circular points at infinity. See also bicircular.
1147:
1. The canonical series is the linear series of the canonical line bundle
425:
7089:
7040:
6962:
6940:
6686:
6643:
6450:
6410:
6381:
6304:
6234:
6123:
5899:
A generator of a scroll (ruled surface) that meets its consecutive generator. See (
5711:
5237:
4890:
4866:
4526:
3649:
The join of two linear spaces is the smallest linear space containing both of them.
3599:
3437:
3430:
3153:
An element of a homaloidal system, in particular the image of a hyperlpane under a
3013:
2882:
2871:
1589:
1542:
1151:
858:
770:
555:
470:
352:
5087:, formed by adding inverses to all functions that do not vanish identically on it.
3483:
is a transformation of order 2 exchanging the inside and outside of a circle. See
7107:
7085:
7011:
6909:
6855:
6778:
6745:
6725:
6721:
6596:
6564:
6532:
6500:
6468:
6454:
6428:
6414:
5632:
5430:
5416:
5182:
4216:
2900:
2875:
2251:
1340:
1265:
901:
1. A bielliptic curve is a branched double cover of an elliptic curve.
716:
590:
6816:
5726:, vol 1, p. 33) A syzygy is a linear relation between points in an affine space.
5067:
is a degree 5 class 3 contravariant of a plane cubic introduced by Cayley (
1687:
2. A subset of a vector space closed under multiplication by scalars.
6870:
6789:
6546:
Principles of geometry. Volume 5. Analytical principals of the theory of curves
6386:
6276:
6047:
5846:
4144:
3928:, given by the zeros of elements of a vector space of sections of a line bundle
3813:
3235:
3066:
2506:
2434:
is a conic containing 11 special points associated to four points and a line. (
2008:
is an archaic term for a node, a double point with distinct tangent directions.
1066:
688:
402:
395:
7093:
6247:
to the dimension when all higher cohomology groups vanish. See superabundance.
5376:
1. A line intersecting a variety in 2 points, or more generally an
4724:
is the line corresponding to a point under a polarity of the projective plane.
4203:
A singularity of a curve where a node and a cusp coincide at the same point. (
3884:
is a curve traced by a point on a circle rolling around a similar circle. See
7121:
7077:
7054:
6974:
6889:
6698:
6672:
6657:
6629:
6607:
6331:
is 4 less than the Euler characteristic of a non-singular projective surface.
6059:
5625:
is the locus of the singular points of the polar quadrics of a hypersurface.
5616:
5426:
5420:
5365:
5276:
4586:
on which the intersections of pairs of sides of two perspective triangles lie
4241:
4227:
3721:
3269:
2859:
2719:
1. A homogeneous polynomial in several variables. Same as quantic.
2625:
2399:
2395:
1232:
1195:
1078:
92:
7000:, Oxford Science Publications, The Clarendon Press Oxford University Press,
6949:-dimensionalen Verallgemeinerungen der fundamentalen Anzahlen unseres Raums"
4439:
1. Meeting at the line or plane at infinity, as in parallel lines
3363:
The dimension of the first cohomology group of the line bundle of a divisor
2313:
1. A 0-dimensional singularity of multiplicity 2, such as a node.
684:
is roughly a vector space where one has forgotten which point is the origin.
100:
7045:
6993:
6690:
6648:
5842:
5812:
5791:
4996:
4157:
4018:
3540:
3251:
if it has order 2, in which case it has an isolated fixed point called its
3119:
2948:
2815:
is used for linear systems, and the letter γ is used for algebraic systems.
1575:
1519:
774:
681:
5518:
is one with a regular local ring, which means roughly that most points of
5490:
One of the 27 points of an elliptic curve of order dividing 6 but not 3. (
4156:
A nodal tangent to a singular point of a curve is one of the lines of its
2734:
An intersection point of two members of a family that is not a base point.
1522:
is an isomorphism from one projective space to another, often to itself. (
1165:
is the map to the projective space of the sections of the canonical bundle
6161:
5858:
5639:
5638:
4. a
Steiner point is one of the 20 points lying on 3 of the
5437:
4482:
4075:
A multiple point is a singular point (one with a non-regular local ring).
3708:
3134:
2621:
2475:
2363:
2293:
variables) which vanishes exactly when the corresponding hypersurface in
1994:
1172:(or variety) is the image of a curve (or variety) under the canonical map
1005:
727:
6220:
are all linearly equivalent. A correspondence need not have a valency. (
5950:
is one that passes through the circular points at infinity with order 3.
5387:
2. A secant variety is the union of the secants of a variety.
3936:
1-A subset of projective space given by points satisfying some condition
2454:
A set of 9 tritangent planes to a cubic surface containing the 27 lines.
1380:
1. A circular point is one of the two points at infinity (1:
6966:
6238:
An embedding of the projective plane in 5-dimensional projective space.
5778:
An invariant of two curves that vanishes if they touch each other. See
5674:
The dimension of the first cohomology group of the corresponding sheaf.
5635:
is a certain embedding of the projective plane into projective 3-space.
5622:
5084:
4745:
1. The point corresponding to a hyperplane under a polarity.
4668:
4085:
3137:
is the group of automorphisms of the Hesse configuration, of order 216.
3059:
2889:
2356:
2236:
1. A differential of the first kind is a holomorphic 1-form.
996:
Homogeneous in each of two sets of variables, as in bihomogeneous form.
979:
7062:
6706:
6665:
5754:
is a point of a curve where two branches meet in the same direction. (
3881:
3348:
A linear subspace of projective space of codimension 1. Same as prime.
2827:, p.204) or more generally an element of some family of linear spaces.
165:
5666:
An abstract surface together with an embedding into projective space.
5233:
3340:
A point where the tangent space meets with order higher than normal.
3177:, p. 442) When the linear system has dimension 2 or 3 it is called a
2478:
is the curve traced by a point of a disc rolling along another disc.
1343:
is the union of the chords and tangent spaces of a projective variety
1105:
7026:
6944:
6062:
is a degree 3 embedding of the projective line in projective 3-space
4377:
A tangent plane of a space curve having third order contact with it.
2652:
A double point that is also a point of inflexion of both branches. (
2529:
A contravariant defined by Sylvester depending on an invariant. See
2316:
One of the two points fixed by an involution of a projective line. (
2305:
A 1-dimensional singularity, usually of a surface, of multiplicity 2
5735:
4. A global syzygy is a resolution of a module or sheaf.
5651:
5064:
4619:
4299:
with the plane at infinity. All points of the ombilic are non-real.
3496:
2620:
3. (Adjective) For the term "flat" in scheme theory see
1281:
1. A special point associated with some geometric object
1240:
1050:
2. For a bipunctual conic with respect to 3 points see
369:
5682:
The zeros of the determinant of a symmetric matrix of linear forms
5403:
An intersection of two primes (hyperplanes) in projective space. (
5140:
2. A labeled or finite ordered set of points on a line.
4454:
The number of connected components of a real algebraic curve. See
2923:-dimensional variety is the number of free intersection points of
2410:
An effective cycle or divisor is one with no negative coefficients
2352:
is the set of hyperplanes, considered as another projective space.
737:
One of a pair of points constructed from two foci of a curve. See
5751:
5192:
4. Defined everywhere, as in regular (birational) map.
3304:
whose tangent cone is a single line meeting the curve with order
2636:
A double point that is also a point of inflexion of one branch. (
2542:
2258:
of a conic in regard to two points is defined in a similar way. (
2072:
is a quartic surface passing doubly through the absolute conic. (
2069:
2005:
1613:
1423:
4088:. A point has multiplicity 1 if and only if it is non-singular.
3076:
2. The Hessian line is a line associated to 3 points
2951:
is a variety parameterizing linear subspaces of projective space
2594:
A facultative point is one where a given function is positive. (
2575:
if it is transformed into a point of the other surface, and an
1957:* its dual, that is invariant under the special linear group of
1828:* its dual, that is invariant under the special linear group of
1656:* its dual, that is invariant under the special linear group of
6308:
A degree 4 genus 6 plane curve with nodes at the 6 points of a
5240:
of two binary forms, that vanishes if they have a common root.
4795:
4296:
2422:) and all lines though a point on the axis (called its center).
1740:
1600:
Reducible (meaning having more than one irreducible component).
1410:
2. Passing through the vertices of something, as in
1218:
is the envelope of light rays from a point reflected in a curve
874:
629:
5216:
A parameter space or moduli space for some family of varieties
4671:
of a variety is the dimension of the space of sections of the
3511:
1. A transformation whose square is the identity.
3499:
is a curve obtained by unrolling a string around a curve. See
1788:
1. A bihomogeneous polynomial in dual variables of
1588:
3. The (line) complex group is an old name for the
4219:
if the linear system defining the embedding is complete; see
1728:
608:
is roughly Euclidean geometry without the parallel postulate.
5668:
4419:
is the configuration of 9 lines and 9 points that occurs in
2048:
is a singular point of a curve whose tangent cone is a line.
7084:, Classics in Mathematics, vol. 61, Berlin, New York:
4638:
1. For Plücker characteristic see characteristic
3130:
is the configuration of inflection points of a plane cubic.
2418:
A collineation that fixes all points on a line (called its
2208:
2. (Noun) The envelope of the normals of a curve
1360:
A component of a real algebraic curve. A circuit is called
1154:
is the line bundle of differential forms of highest degree.
857:
Having nodes at the two circular points at infinity, as in
398:
were, even if "trope" was not precisely defined in general.
6046:, p.202) The word is mostly used for a tangent space of a
5440:
is a cubic hypersurface in 4-dimensional projective space.
4929:
A number depending on two branches at a point, defined by
2545:
is the envelope of the normal lines of a plane curve. See
2222:
of a curve is the surface consisting of its tangent lines.
2169:
2. The number of points of a divisor on a curve
1585:
2. (Adjective.) Related to the complex numbers.
931:+1-dimensional space of even-cardinality subsets of a set
7032:
Philosophical Transactions of the Royal Society of London
6678:
Philosophical Transactions of the Royal Society of London
6675:(1869), "A Memoir on the Theory of Reciprocal Surfaces",
6635:
Philosophical Transactions of the Royal Society of London
4705:–2, ... formed from a point and a hypersurface of degree
3005:
2. A harmonic cubic is an elliptic curve with
2036:
A curve together with an embedding into projective space.
1772:
A correspondence between a projective space and its dual.
99:
in the beginning of the century, and later formalized by
6262:
A 3-dimensional linear system. See "net" and "pencil". (
6126:, in other words birational to the projective line. See
5986:
Coordinates based on distance from sides of a triangle:
4782:-gonal) curve is a curve together with a map (of degree
3222:
is a line associated to two related ranges of a conic. (
3188:
2. Homaloidal means similar to a flat plane.
1426:
is the curve generated from two curves and a point. See
1403:
1. Having edges tangent to some curve, as in
1120:
Meeting a curve at the tangency points of its bitangents
1108:
is a line that is tangent to a curve at two points. See
2579:
if it is transformed into a curve of the other surface.
1925:, ... and the coefficients of some homogeneous form in
1796:, ... and the coefficients of some homogeneous form in
1186:
is a divisor of a section of the canonical line bundle.
4557:
The integral of a differential form over a submanifold
4107:
is the group of divisors module numerical equivalence.
3625:
The set of free double points of a pencil of curves. (
3324:
is a curve with a degree 2 map to the projective line.
2803:
A linear or algebraic system of divisors of dimension
2606:
holomorphic or regular (when applied to differentials)
2285:
The invariant (on the vector space of forms of degree
2150:, ... are the multiplicities of its singular points. (
401:
Algebraic geometry was often implicitly done over the
4953:
All components are of the same dimension. Now called
4240:
4. Local rings are integrally closed; see
3730:
3041:
6. For harmonically conjugate conics see (
2056:
The locus of the focal points of a family of planes (
1985:
is a birational map from a projective space to itself
503:
437:
5236:
of two polynomials, given by the determinant of the
4183:= 0, usually with the determinant of the Hessian of
904:
2. A bielliptic surface is the same as a
664:–1 on the adjoint. Sometimes the multiple points of
5380:-dimensional projective space meeting a variety in
5356:, p.8). Possibly something to do with base points.
5055:
Degree 5, especially a degree 5 projective variety.
5039:
Depending on four variables, as in quaternary form.
4748:
2. A singularity of a rational function.
4431:
A point of a variety that also lies in the Hessian.
3868:A lemniscate is a curve resembling a figure 8. See
2099:
2. (Noun) A degree 10 projective variety
927:
over the field with 2 elements, consisting of the 2
5502:Degree 6, especially a degree 6 projective variety
5479:2. (Noun) A degree 7 projective variety
4283:2. (Noun) A degree 8 projective variety
4215:1. A subvariety of projective space is
3784:
2016:Degree 3, especially a degree 3 projective variety
1202:that vanishes when the form is a sum of powers of
1128:A non-planar hexagon whose three diagonals meet. (
527:
461:
6926:(4th ed.), Dublin, Hodges, Figgis, and Co.,
6923:Lessons introductory to the modern higher algebra
6632:(1857), "A Memoir on Curves of the Third Order",
4709:by polarizing the equation of the hypersurface. (
3637:The linear system generated by Jacobian curves. (
3288:Essentially a blow-up of a curve at a point. See
1997:is an invariant of 4 points on a projective line.
573:The deviation of a curve from circular form. See
7119:
6164:if it is finitely covered by a rational variety.
6042:is a singular (meaning special) tangent space. (
5151:2. Defined over the rational numbers.
5133:1. The set of all points on a line. (
4802:. The precise meaning seems to be controversial.
4470:, the line determined by 6 points of a conic in
3840:such that the base locus of a generic pencil of
3613:The locus of double points of curves of a net. (
3429:1. Having vertices on a curve, as in
2617:2. (Adjective) Having curvature zero.
923:is an element of the vector space of dimension 2
6347:Glossary of arithmetic and Diophantine geometry
5333:2. A certain plane curve of degree (
5001:
4821:Having either no solutions or infinitely many (
4691:1. (Adjective) Related by a polarity
3672:-dimensional projective space. (Sylvester
3196:1. Having the same invariants. See
2919:The grade of a linear system of divisors on an
6357:Glossary of differential geometry and topology
5167:1. A regular surface is one whose
4798:is a corollary, especially in geometry, as in
3300:A singularity of a curve of some multiplicity
3012:3. Satisfying some analogue of the
1268:is a conic or quadric used to define a metric.
6617:The Cambridge and Dublin Mathematical Journal
6402:Principles of geometry. Volume 1. Foundations
5341:–2) constructed from a plane curve of degree
5148:1. Birational to projective space.
4869:with respect to an algebraic curve of degree
2911:-dimensional non-singular projective variety.
2903:is the dimension of the space of holomorphic
838:is a point common to all members of a family.
5891:2. (Noun) A 3-dimensional variety
3993:2. A model for a field extension
2189:A desmic system is a configuration of three
1917:1. A bihomogeneous polynomial in
1198:is an invariant of a binary form of degree 2
939:elements, modulo the 1-dimensional space {0,
6795:Classical Algebraic Geometry: a modern view
6200:The valence or valency of a correspondence
5888:1. (Adjective) Three-dimensional
5174:2. Having no singularities; see
5159:A line, especially one in a family of lines
4970:
3964:The meet of two sets is their intersection.
3436:2. Tangent to some lines, as in
2462:A curve tangent to a family of curves. See
2398:is a point of intersection of 3 lines on a
1284:2. The center of a perspectivity
1179:is the divisor class of a canonical divisor
6988:
6367:Glossary of Riemannian and metric geometry
6321:
6263:
6221:
6154:
6084:
6018:A line meeting a variety in 3 points. See
5975:
5900:
5551:
5404:
5256:
5210:
5122:
5115:
5028:
5008:
4999:is a line meeting something in four points
4958:
4910:
4894:
4854:
4822:
4734:
4710:
4603:
4326:
4312:
4254:
4234:
4161:
4064:
4053:
4048:
3953:
3638:
3626:
3614:
3380:
3276:>0 with the maximum possible number 84(
3170:
2936:
2932:
2928:
2839:
2824:
2747:
2708:
2696:
2680:
2673:
2375:
2202:
2151:
2073:
2057:
2025:
1855:
1716:
1681:
1579:
1535:
1523:
1492:
1457:
1446:
1439:
1301:
1024:
808:
750:
669:
632:is an isolated point of a real curve. See
536:
384:
359:
159:
7044:
7021:
6788:
6647:
6072:
5691:
5670:superabundance of a divisor on a surface.
5460:
5314:
5267:Inverse (of a function or birational map)
5072:
4767:
4646:
4325:is the order (degree) of its homaloids. (
3853:
3673:
3605:2. A Jacobian curve; see below
3024:
1975:
1552:is 4 points and the 6 lines joining pairs
1255:
1093:
1069:is a rational map with rational "inverse"
944:
334:
115:
79:Learn how and when to remove this message
6939:
6720:
5980:
5352:3. For satellite points see (
5346:
4930:
4878:
4443:
4116:
3857:
3695:One of the 60 points lying on 3 of the
3385:
3334:
3309:
3174:
2998:, and the points of one pair are called
2969:
1970:
1499:
1452:3. The class of a surface in
1369:
1317:
1309:
916:1. Split into two equal parts
474:
143:
42:This article includes a list of general
7076:
6961:, Springer Berlin / Heidelberg: 26–51,
6898:, New York: Hodges, Foster and Figgis,
6755:
5353:
5134:
4942:
4545:A union of 5 planes, in particular the
3785:{\displaystyle x^{3}y+y^{3}z+z^{3}x=0.}
3069:, or a variety associated with it. See
1559:is 4 lines meeting in pairs in 6 points
1287:3. The center of an isologue
147:
14:
7120:
6919:
6888:
6865:
6832:
6671:
6628:
6606:
6574:
6542:
6438:
6398:
6377:List of complex and algebraic surfaces
6142:
6127:
6103:
6043:
6007:
5796:
5779:
5767:
5755:
5723:
5655:
5626:
5599:
5587:
5575:
5571:
5491:
5327:
5104:
5068:
4842:
4675:th power of the canonical line bundle.
4615:
4510:
4455:
4386:
4366:
4354:
4204:
4192:
4131:
3979:
3905:
3885:
3869:
3685:
3676:, Glossary p. 543–548) Archaic.
3500:
3484:
3406:
3357:
3289:
3272:is a complex algebraic curve of genus
3223:
3204:
3197:
3070:
3042:
3035:
2701:
2692:
2653:
2641:
2637:
2595:
2546:
2530:
2479:
2463:
2435:
2317:
2259:
2215:, one that can be unrolled to a plane
2155:
1867:
1754:
1744:
1739:1. A conjugate point is an
1617:
1480:
1427:
1331:A line joining two points of a variety
1245:
1129:
1109:
1051:
1036:
967:
955:
862:
738:
633:
617:
574:
554:1. An archaic name for the
155:
151:
139:
135:
123:
119:
6895:A treatise on the higher plane curves
6872:Quartic surfaces with singular points
6510:
6478:
5922:An invariant depending on two forms.
4683:A family of lines with a common point
4390:
4097:
4005:together with an isomorphism between
3583:is called the center of the isologue.
3418:
2823:One of the lines of a ruled surface (
2424:
2276:directrix of a rational normal scroll
1081:is a regular map with regular inverse
1035:Having two connected components. See
131:
127:
6727:A treatise on algebraic plane curves
6282:
5893:
5811:Depending on three variables, as in
5642:associated with 6 points on a conic.
5482:3. (Noun) A degree 7 form
4009:and its field of rational functions.
3699:associated with 6 points on a conic.
2728:
2577:exceptional curve of the second kind
1122:
97:Italian school of algebraic geometry
28:
6296:
6226:
6006:Having three connected components.
5592:
4859:
4521:A 1-dimensional linear system. See
4379:
4371:
4365:Kiss; to meet with high order. See
4029:
3898:
2573:exceptional curve of the first kind
2096:1. (Adjective) Degree 10
1616:of a circle and another curve. See
1388:: 0) through which all circles pass
763:
721:
24:
6998:Introduction to algebraic geometry
6840:, Cambridge Mathematical Library,
6612:"On the singularities of surfaces"
6160:2. A variety is called
5644:
5556:
5484:
5476:1. (Adjective) Degree 7
4889:An old term for a hyperplane in a
4425:
4337:An ordinary point of multiplicity
4280:1. (Adjective) Degree 8
4022:
3793:
3631:
3411:
3262:
2893:
1333:
1004:Depending on two variables, as in
652:is a curve such that any point of
469:. This notation was introduced by
48:it lacks sufficient corresponding
25:
7149:
6268:
6122:A unicursal curve is one that is
5772:
5442:
5415:1. Named after either
5181:3. Symmetrical, as in
5021:
4295:which is the intersection of any
4136:
3966:
3805:
3607:
3391:A point on a blow up of a variety
2496:
2211:3. (Noun) Short for a
1872:
1541:2. A scheme is called
1294:
497:A family or variety of dimension
6581:, Cambridge Library Collection,
6575:Baker, Henry Frederick (1933b),
6549:, Cambridge Library Collection,
6543:Baker, Henry Frederick (1933a),
6517:, Cambridge Library Collection,
6485:, Cambridge Library Collection,
6445:, Cambridge Library Collection,
6439:Baker, Henry Frederick (1922b),
6405:, Cambridge Library Collection,
6399:Baker, Henry Frederick (1922a),
5255:-dimensional projective space. (
5125:, p.193) See order, class, type.
5077:
4559:
4246:
3918:
3689:
3314:
3257:
3002:with respect to the other pair.
2388:
2183:
2050:
1782:
1689:
1397:
1188:
990:
699:An automorphism of affine space.
548:
405:(or sometimes the real numbers).
175:
33:
18:Postulation (algebraic geometry)
6757:Coxeter, Harold Scott MacDonald
6511:Baker, Henry Frederick (1925),
6479:Baker, Henry Frederick (1923),
6352:Glossary of commutative algebra
6166:
5916:
5835:
5784:
5760:
5307:
4989:
4915:
4077:
3836:of plane curves of some degree
3826:
3817:A quartic surface with 16 nodes
3619:
3551:Given a Cremoma transformation
3529:
2941:
2488:
2307:
2299:
2279:
2230:
2142:is the degree of the curve and
1545:if the map to a point is proper
1512:
1114:
1047:1. Having two points
779:
485:A family of dimension 1, 2, ...
310:
168:
7039:, The Royal Society: 407–548,
6875:, Cambridge University Press,
6685:, The Royal Society: 201–229,
6642:, The Royal Society: 415–446,
6342:Glossary of algebraic geometry
6147:
5952:
5940:
5924:
5880:All poles are simple (order 1)
5851:
5650:One of Cayley's names for the
5395:All residues at poles are zero
5389:
5301:Projective space of dimension
4923:
4847:
4760:
4576:
4539:
4489:with respect to a pedal point
4448:
4309:degree of an algebraic variety
3282:
3190:
2752:
2646:
2588:
2551:
2515:
2468:
2195:
1987:
1847:
1774:
1622:
1485:
811:, p.274) Similar to directrix.
479:
431:Projective space of dimension
320:
13:
1:
6392:
6132:
6096:
6024:
6000:
5874:
5863:
5676:
5609:
5447:
5033:
4835:
4677:
4651:
4574:The center of a perspectivity
4568:
4321:3. The order of a
4043:with a point of multiplicity
4001:is a projective variety over
3862:
3515:that are involutions include
3505:
3393:
3342:
3209:
3159:
2664:Short for point of inflection
2600:
2483:
2322:
2110:2. The deficiency
2101:
2018:
1901:Having the same singularities
1895:
1860:
1709:
1666:
1056:
1041:
960:
895:
879:
851:
787:
691:is a variety in affine space.
610:
528:{\displaystyle 1,2,\ldots ,n}
462:{\displaystyle 1,2,\ldots ,n}
305:
6455:10.1017/CBO9780511718298.009
6415:10.1017/CBO9780511718267.007
6362:Glossary of invariant theory
6116:
6108:
6012:
5968:
5882:
5824:
5704:
5319:
5226:
5003:quadro-cubic, quadro-quartic
4935:
4772:
4755:
4750:
4197:
3904:Projective coordinates. See
3658:
3473:
3465:
3423:
3398:
3326:
3294:
2817:
2509:cubic is a cubic curve with
2448:
2404:
2272:directrix of a conic section
2264:
2171:
1911:
1733:
1594:
1504:
1289:
1141:
1098:
1086:
1071:
1029:
731:
701:
567:
167:
7:
6335:
5992:
5960:
5684:
5528:
5470:
5397:
5218:
5142:
5096:
5075:, p.157). See also pippian.
5057:
4815:
4726:
4614:Introduced by Cayley (
4497:such that the line through
4433:
4359:
4331:
4069:
3945:
3678:
3592:
3579:) are collinear. The point
3545:
3489:
3442:
3228:
3147:
2988:
2630:
2523:
2456:
2440:
2244:
1949:is some symmetric power of
1839:
1820:is some symmetric power of
1719:, p.238, 288). See complex.
1701:
1648:is some symmetric power of
1602:
1528:
1405:circumscribed quadrilateral
1374:
1304:, p.189) In particular the
1225:
887:
813:
743:
693:
579:
10:
7154:
6842:Cambridge University Press
6803:Cambridge University Press
6763:(2nd ed.), New York:
6583:Cambridge University Press
6551:Cambridge University Press
6519:Cambridge University Press
6487:Cambridge University Press
6447:Cambridge University Press
6407:Cambridge University Press
6302:
6288:
6274:
6240:
6232:
6194:
6189:
6052:
6050:touching it along a conic.
5805:
5744:
5660:
5615:1. Named after
5604:
5564:
5261:
5202:
5194:
5161:
5049:
5041:
5013:
4981:
4941:For proximate points see (
4630:
4624:
4608:
4347:
4285:
4142:
4011:
3972:
3874:
3811:
3803:of two curves on a surface
3717:is a certain cubic surface
3555:, the isologue of a point
3052:
2846:
2736:
2535:
2412:
2350:dual of a projective space
2225:5. Flat, as in
2090:
2062:
1999:
1886:is an algebraic subset of
1612:is the curve given by the
1568:
1470:
1416:
1354:
1238:
1208:
1009:
972:
877:is a curve with two cusps.
709:
660:has multiplicity at least
648:is a curve, an adjoint of
638:
420:
372:to figure out the meaning.
7138:Glossaries of mathematics
7094:10.1007/978-3-642-61991-5
6372:Glossary of scheme theory
5816:
5716:
5696:
5504:
5496:
5465:
5370:
5358:
4899:
4788:
4551:
4531:
4515:
4460:
4402:
4307:1. Now called
4209:
4033:
3926:linear system of divisors
3910:
3715:Klein icosahedral surface
3537:irregularity of a surface
3525:De Jonquières involutions
2160:
1903:
1766:
1465:
1345:
1275:
1270:
1220:
1017:
998:
966:Same as fleflecnode. See
867:
755:
674:
622:
180:
6920:Salmon, George (1885) ,
6867:Jessop, Charles Minshall
6838:Kummer's quartic surface
6761:Introduction to Geometry
6208:such that the divisors
6174:
6064:
6032:
5932:
5905:
5544:
5409:
5275:Covered by lines, as in
5269:
5127:
4972:quadratic transformation
4883:
4685:
4588:
4475:
4421:Pappus's hexagon theorem
4301:
4274:
4266:
4150:
3984:
3930:
3701:
3139:
3047:
2953:
2913:
2864:
2685:
2666:
2366:is a number of the form
2085:
2030:
2010:
1941:* for some vector space
1721:
1640:* for some vector space
1582:, p.236) See congruence.
1574:1. (Noun.) A
1432:
1393:circular algebraic curve
1325:
910:
795:
300:
160:Semple & Roth (1949)
7023:Sylvester, James Joseph
6732:Oxford University Press
6722:Coolidge, Julian Lowell
6329:Zeuthen–Segre invariant
6323:Zeuthen–Segre invariant
6204:on a curve is a number
6077:
5580:
5536:
5212:representative manifold
5108:
4947:
4907:projective hypersurface
4825:, p.186). For example,
4739:
4493:is the locus of points
4345:distinct tangent lines.
4341:of a curve is one with
4166:
4109:
4055:monoidal transformation
3958:
3954:Semple & Roth (1949
3890:
3643:
3513:Cremona transformations
3381:Semple & Roth (1949
2811:on a curve. The letter
2713:
2658:
2608:
2376:Semple & Roth (1949
2342:
2334:
2038:
2026:Semple & Roth (1949
1674:
1526:, p.6) See correlation.
1306:Plücker characteristics
828:
800:
63:more precise citations.
7046:10.1098/rstl.1853.0018
6691:10.1098/rstl.1869.0009
6649:10.1098/rstl.1857.0021
6316:
6264:Semple & Roth 1949
6256:
6222:Semple & Roth 1949
6155:Semple & Roth 1949
6085:Semple & Roth 1949
5976:Semple & Roth 1949
5901:Semple & Roth 1949
5832:complete quadrilateral
5552:Semple & Roth 1949
5405:Semple & Roth 1949
5345:and a generic point. (
5257:Semple & Roth 1949
5245:Cremona transformation
5153:
5123:Semple & Roth 1949
5116:Semple & Roth 1949
5029:Semple & Roth 1949
5009:Semple & Roth 1949
4959:Semple & Roth 1949
4911:Semple & Roth 1949
4895:Semple & Roth 1949
4855:Semple & Roth 1949
4823:Semple & Roth 1949
4735:Semple & Roth 1949
4711:Semple & Roth 1949
4604:Semple & Roth 1949
4327:Semple & Roth 1949
4323:Cremona transformation
4313:Semple & Roth 1949
4255:Semple & Roth 1949
4235:Semple & Roth 1949
4162:Semple & Roth 1949
4121:
4065:Semple & Roth 1949
4049:Semple & Roth 1949
3786:
3639:Semple & Roth 1949
3627:Semple & Roth 1949
3615:Semple & Roth 1949
3171:Semple & Roth 1949
3167:Cremona transformation
3155:Cremona transformation
3016:, as in harmonic form.
2937:Semple & Roth 1949
2933:Semple & Roth 1949
2929:Semple & Roth 1949
2840:Semple & Roth 1949
2835:
2825:Semple & Roth 1949
2748:Semple & Roth 1949
2709:Semple & Roth 1949
2697:Semple & Roth 1949
2681:Semple & Roth 1949
2674:Semple & Roth 1949
2374:where ε has square 0.
2203:Semple & Roth 1949
2152:Semple & Roth 1949
2074:Semple & Roth 1949
2058:Semple & Roth 1949
1983:Cremona transformation
1977:Cremona transformation
1878:A correspondence from
1856:Semple & Roth 1949
1812:for some vector space
1717:Semple & Roth 1949
1682:Semple & Roth 1949
1580:Semple & Roth 1949
1557:complete quadrilateral
1536:Semple & Roth 1949
1524:Semple & Roth 1949
1493:Semple & Roth 1949
1458:Semple & Roth 1949
1447:Semple & Roth 1949
1440:Semple & Roth 1949
1302:Semple & Roth 1949
1025:Semple & Roth 1949
809:Semple & Roth 1949
751:Semple & Roth 1949
670:Semple & Roth 1949
537:Semple & Roth 1949
529:
463:
385:Semple & Roth 1949
380:
360:Semple & Roth 1949
330:
295:
290:
285:
280:
275:
270:
265:
260:
255:
250:
245:
240:
235:
230:
225:
220:
215:
210:
205:
200:
195:
190:
185:
109:Alexander Grothendieck
6954:Mathematische Annalen
6765:John Wiley & Sons
5988:Trilinear coordinates
5982:trilinear coordinates
5845:is a special kind of
5522:are simple points of
4865:Laguerre defined the
4547:Sylvester pentahedron
4389:, vol 2, p. 33) and (
4221:rational normal curve
3852:–1 collinear points (
3844:is the base locus of
3787:
3559:is the set of points
3387:infinitely near point
3336:hyperosculating point
3280:–1) of automorphisms.
2830:
906:hyperelliptic surface
845:ρ is the rank of the
530:
464:
376:
325:
6251:
6184:
6091:
5739:
5288:
5283:
5091:
4965:
4622:. See also quippian.
4523:pencil (mathematics)
4417:Pappus configuration
4410:Pappus of Alexandria
4397:
4261:
4092:
4039:A surface of degree
3975:Möbius configuration
3940:
3821:
3728:
3653:
3587:
3352:
3234:1. As in
2983:
2774:
2769:
2583:
2382:
2080:
1707:Having the same foci
1412:circumscribed circle
1136:
823:
543:
501:
435:
7133:History of geometry
6834:Hudson, R. W. H. T.
6310:complete quadrangle
5912:Developable surface
5871:complete quadrangle
5798:tangential equation
5071:) and discussed by
4549:of a cubic surface.
3801:intersection number
3664:An intersection of
3517:Bertini involutions
3421:, vol 3, p. 52, 88)
3367:; often denoted by
3359:index of speciality
3322:hyperelliptic curve
3128:Hesse configuration
3021:harmonic polar line
3000:harmonic conjugates
2979:in the usual sense.
2703:foliate singularity
2691:A focal point. See
2563:exceptional divisor
2340:A set of two points
2330:Schläfli double six
2227:developable surface
2220:tangent developable
2213:developable surface
1550:complete quadrangle
1163:canonical embedding
370:classical education
169:Contents:
7128:Algebraic geometry
7082:Algebraic surfaces
6967:10.1007/BF01443568
6790:Dolgachev, Igor V.
6020:trisecant identity
5998:Having three nodes
5958:Having three cusps
5436:3. The
5279:. See also scroll.
5232:1. The
5187:regular polyhedron
5176:regular local ring
4905:An old term for a
4618:). Now called the
4415:2. The
4179:of a hypersurface
4105:Néron–Severi group
4099:Néron–Severi group
3856:, theorem 7.3.5) (
3782:
3720:3. The
3713:2. The
3598:1. The
3521:Geiser involutions
3247:). It is called a
3220:axis of homography
3133:6. The
3126:5. The
3118:4. The
3045:, vol 2, p. 122).
3019:4. The
2858:3. The
2744:degrees of freedom
2432:eleven-point conic
2426:eleven-point conic
2355:2. The
2348:1. The
2218:4. The
2179:Desargues' theorem
2138:–2)/2 –..., where
1762:harmonic conjugate
1760:4. For
1672:Meeting at a point
1175:5. The
1157:3. The
1150:2. The
1054:, vol 2, p. 123).
952:bifid substitution
847:Neron–Severi group
841:2. The
525:
459:
7103:978-3-540-58658-6
7007:978-0-19-853363-4
6941:Schubert, Hermann
6933:978-0-8284-0150-0
6905:978-1-4181-8252-6
6882:978-1-112-28262-1
6851:978-0-521-39790-2
6812:978-1-107-01765-8
6774:978-0-471-50458-0
6741:978-0-486-49576-7
6592:978-1-108-01782-4
6560:978-1-108-01781-7
6528:978-1-108-01780-0
6496:978-1-108-01779-4
6464:978-1-108-01778-7
6424:978-1-108-01777-0
6291:Weierstrass point
6284:Weierstrass point
5948:tricircular curve
5938:A set of 3 points
5895:torsal generator.
5822:A set of 4 points
5590:, vol 1, p. 109)
4827:Poncelet's porism
4807:Poncelet's porism
4800:Poncelet's porism
4716:4. A
4584:Desargues theorem
4537:A set of 5 points
4272:A set of 8 points
4134:, vol 1, p. 133)
3668:hypersurfaces in
3249:harmonic homology
3218:2. An
3145:A set of 6 points
3038:, vol 1, p. 133)
2742:Dimension, as in
2730:free intersection
2724:differential form
2569:exceptional curve
2567:2. An
2559:exceptional curve
2505:2. An
2191:desmic tetrahedra
1845:In the same plane
1391:2. A
1184:canonical divisor
1124:Brianchon hexagon
687:2. An
620:, vol 6, p. 157)
606:Absolute geometry
599:absolute polarity
563:commutative group
561:2. A
105:Jean-Pierre Serre
89:
88:
81:
16:(Redirected from
7145:
7114:
7073:
7048:
7018:
6985:
6936:
6916:
6885:
6862:
6829:
6828:
6827:
6821:
6815:, archived from
6800:
6785:
6752:
6717:
6668:
6651:
6625:
6603:
6571:
6539:
6507:
6475:
6435:
6382:List of surfaces
6305:Wirtinger sextic
6298:Wirtinger sextic
6235:Veronese surface
6228:Veronese surface
5712:syzygetic pencil
5631:3. A
5621:2. A
5594:stationary point
5425:2. A
5251:correlations of
5243:2. A
5238:Sylvester matrix
4891:projective space
4867:power of a point
4861:power of a point
4831:Steiner's porism
4811:Steiner's porism
4794:1. A
4778:A polygonal (or
4641:2. A
4527:Lefschetz pencil
4472:Pascal's theorem
4381:outpolar quadric
4373:osculating plane
3982:, vol 1, p. 62)
3900:line coordinates
3791:
3789:
3788:
3783:
3772:
3771:
3756:
3755:
3740:
3739:
3600:Jacobian variety
3438:inscribed circle
3431:inscribed figure
3226:, vol 2, p. 16)
3065:1. A
3030:5. A
3014:Laplace equation
2975:2. A
2959:1. A
2883:arithmetic genus
2872:genus of a curve
2843:
2799:
2798:
2788:
2787:
2722:2. A
2438:, vol 2, p. 49)
2362:3. A
2262:, vol 2, p. 26)
1757:, vol 2, p. 26)
1590:symplectic group
1562:5. A
1555:4. A
1548:3. A
1510:On the same line
1483:, vol 2, p. 66)
1264:4. A
1250:2. A
1182:6. A
1168:4. A
1152:canonical bundle
1132:, vol 1, p. 47)
1077:1. A
1065:2. A
1015:Having two nodes
950:3. A
919:2. A
885:Having two cusps
859:bicircular curve
834:1. A
771:arithmetic genus
765:arithmetic genus
723:anharmonic ratio
656:of multiplicity
556:symplectic group
534:
532:
531:
526:
468:
466:
465:
460:
388:
353:Veronese surface
338:
170:
114:Dolgachev (
84:
77:
73:
70:
64:
59:this article by
50:inline citations
37:
36:
29:
21:
7153:
7152:
7148:
7147:
7146:
7144:
7143:
7142:
7118:
7117:
7104:
7086:Springer-Verlag
7008:
6990:Semple, John G.
6934:
6906:
6883:
6852:
6825:
6823:
6819:
6813:
6798:
6775:
6742:
6593:
6561:
6529:
6497:
6465:
6425:
6395:
6338:
6324:
6319:
6307:
6299:
6293:
6285:
6279:
6271:
6259:
6254:
6243:
6237:
6229:
6197:
6192:
6187:
6177:
6169:
6150:
6135:
6119:
6111:
6099:
6094:
6080:
6067:
6055:
6035:
6027:
6015:
6003:
5995:
5983:
5971:
5963:
5955:
5943:
5935:
5927:
5919:
5908:
5896:
5885:
5877:
5866:
5854:
5838:
5827:
5819:
5808:
5799:
5787:
5775:
5763:
5747:
5742:
5719:
5707:
5699:
5687:
5679:
5671:
5663:
5647:
5646:Steiner–Hessian
5633:Steiner surface
5612:
5607:
5595:
5583:
5567:
5559:
5558:special divisor
5547:
5539:
5531:
5507:
5499:
5487:
5486:sextactic point
5473:
5468:
5450:
5445:
5431:Segre embedding
5417:Beniamino Segre
5412:
5400:
5392:
5373:
5361:
5322:
5310:
5298:
5297:
5286:
5272:
5264:
5229:
5221:
5213:
5205:
5197:
5183:regular polygon
5164:
5156:
5145:
5130:
5111:
5099:
5094:
5080:
5073:Dolgachev (2012
5060:
5052:
5044:
5036:
5024:
5016:
5004:
4992:
4984:
4973:
4968:
4955:equidimensional
4950:
4938:
4926:
4918:
4902:
4886:
4862:
4850:
4838:
4818:
4791:
4775:
4763:
4758:
4753:
4742:
4729:
4688:
4680:
4654:
4635:
4627:
4611:
4591:
4579:
4571:
4562:
4554:
4542:
4534:
4518:
4478:
4463:
4451:
4436:
4428:
4427:parabolic point
4408:1.
4405:
4400:
4393:, vol 3, p. 52)
4382:
4374:
4362:
4350:
4334:
4304:
4288:
4277:
4269:
4264:
4249:
4217:linearly normal
4212:
4200:
4169:
4153:
4147:
4139:
4124:
4112:
4100:
4095:
4080:
4072:
4056:
4036:
4030:#Möbius tetrads
4025:
4024:Moebius tetrads
4014:
3987:
3977:
3969:
3961:
3948:
3943:
3933:
3921:
3913:
3901:
3893:
3877:
3865:
3829:
3824:
3816:
3808:
3796:
3795:Kronecker index
3767:
3763:
3751:
3747:
3735:
3731:
3729:
3726:
3725:
3704:
3692:
3681:
3661:
3656:
3646:
3634:
3633:Jacobian system
3622:
3610:
3595:
3590:
3548:
3532:
3508:
3492:
3476:
3468:
3445:
3426:
3414:
3413:inpolar quadric
3401:
3396:
3388:
3360:
3355:
3345:
3337:
3329:
3317:
3297:
3285:
3265:
3264:Hurwitz surface
3260:
3231:
3212:
3193:
3162:
3150:
3142:
3100:with the lines
3055:
3050:
2991:
2986:
2956:
2944:
2916:
2901:geometric genus
2896:
2895:geometric genus
2876:geometric genus
2867:
2849:
2845:
2837:
2820:
2800:
2797:
2792:
2791:
2790:
2786:
2781:
2780:
2779:
2772:
2755:
2739:
2731:
2716:
2704:
2688:
2669:
2661:
2649:
2633:
2611:
2603:
2591:
2586:
2554:
2538:
2526:
2518:
2499:
2491:
2486:
2471:
2459:
2451:
2443:
2427:
2415:
2407:
2391:
2385:
2345:
2337:
2325:
2310:
2302:
2282:
2267:
2252:director circle
2247:
2233:
2198:
2186:
2174:
2163:
2104:
2093:
2088:
2083:
2065:
2053:
2041:
2033:
2021:
2013:
2002:
1990:
1978:
1914:
1909:An ordered pair
1906:
1898:
1875:
1863:
1850:
1842:
1785:
1777:
1769:
1736:
1724:
1712:
1704:
1692:
1677:
1669:
1625:
1605:
1597:
1571:
1531:
1515:
1507:
1488:
1473:
1468:
1435:
1419:
1400:
1377:
1357:
1348:
1341:chordal variety
1336:
1335:chordal variety
1328:
1297:
1292:
1278:
1273:
1266:Cayley absolute
1243:
1228:
1223:
1211:
1191:
1177:canonical class
1170:canonical curve
1144:
1139:
1125:
1117:
1101:
1089:
1074:
1059:
1044:
1032:
1020:
1012:
1001:
993:
987:
975:
963:
913:
898:
890:
882:
870:
854:
831:
826:
816:
803:
798:
790:
782:
766:
758:
746:
734:
724:
717:ambient variety
712:
704:
696:
677:
641:
625:
613:
591:Cayley absolute
582:
570:
551:
546:
502:
499:
498:
494:
489:{1}, {2}, ...,{
482:
436:
433:
432:
428:
423:
403:complex numbers
390:
382:
340:
332:
323:
318:
317:
316:
315:
171:
144:Coolidge (1931)
85:
74:
68:
65:
55:Please help to
54:
38:
34:
23:
22:
15:
12:
11:
5:
7151:
7141:
7140:
7135:
7130:
7116:
7115:
7102:
7078:Zariski, Oscar
7074:
7019:
7006:
6986:
6937:
6932:
6917:
6904:
6890:Salmon, George
6886:
6881:
6863:
6850:
6830:
6811:
6786:
6773:
6753:
6740:
6718:
6673:Cayley, Arthur
6669:
6630:Cayley, Arthur
6626:
6608:Cayley, Arthur
6604:
6591:
6572:
6559:
6540:
6527:
6508:
6495:
6476:
6463:
6436:
6423:
6394:
6391:
6390:
6389:
6387:List of curves
6384:
6379:
6374:
6369:
6364:
6359:
6354:
6349:
6344:
6337:
6334:
6333:
6332:
6325:
6322:
6318:
6315:
6314:
6313:
6303:Main article:
6300:
6297:
6295:
6289:Main article:
6286:
6283:
6281:
6277:Weddle surface
6275:Main article:
6272:
6270:Weddle surface
6269:
6267:
6260:
6257:
6253:
6250:
6249:
6248:
6244:
6241:
6239:
6233:Main article:
6230:
6227:
6225:
6198:
6195:
6193:
6190:
6186:
6183:
6182:
6181:
6178:
6175:
6173:
6170:
6167:
6165:
6158:
6151:
6148:
6146:
6136:
6133:
6131:
6120:
6117:
6115:
6112:
6109:
6107:
6100:
6097:
6093:
6090:
6089:
6088:
6081:
6078:
6076:
6073:Dolgachev 2012
6068:
6065:
6063:
6056:
6053:
6051:
6048:Kummer surface
6036:
6033:
6031:
6028:
6025:
6023:
6016:
6013:
6011:
6004:
6001:
5999:
5996:
5993:
5991:
5984:
5981:
5979:
5972:
5969:
5967:
5964:
5961:
5959:
5956:
5953:
5951:
5944:
5941:
5939:
5936:
5933:
5931:
5928:
5925:
5923:
5920:
5917:
5915:
5909:
5906:
5904:
5897:
5894:
5892:
5889:
5886:
5883:
5881:
5878:
5875:
5873:
5867:
5864:
5862:
5855:
5852:
5850:
5847:Kummer surface
5839:
5836:
5834:
5828:
5825:
5823:
5820:
5817:
5815:
5809:
5806:
5804:
5800:
5797:
5795:
5788:
5785:
5783:
5776:
5774:tact-invariant
5773:
5771:
5764:
5761:
5759:
5748:
5745:
5741:
5738:
5737:
5736:
5733:
5730:
5727:
5720:
5717:
5715:
5708:
5705:
5703:
5700:
5697:
5695:
5692:Dolgachev 2012
5688:
5685:
5683:
5680:
5677:
5675:
5672:
5669:
5667:
5664:
5661:
5659:
5648:
5645:
5643:
5636:
5629:
5619:
5613:
5610:
5608:
5605:
5603:
5596:
5593:
5591:
5584:
5581:
5579:
5568:
5565:
5563:
5560:
5557:
5555:
5548:
5545:
5543:
5540:
5537:
5535:
5532:
5529:
5527:
5508:
5505:
5503:
5500:
5497:
5495:
5488:
5485:
5483:
5480:
5477:
5474:
5471:
5469:
5466:
5464:
5461:Dolgachev 2012
5457:
5454:
5451:
5448:
5446:
5444:self-conjugate
5443:
5441:
5434:
5423:
5413:
5410:
5408:
5401:
5398:
5396:
5393:
5390:
5388:
5385:
5374:
5371:
5369:
5362:
5359:
5357:
5350:
5349:, p. 159–161)
5331:
5323:
5320:
5318:
5315:Dolgachev 2012
5311:
5308:
5306:
5299:
5293:
5289:
5285:
5282:
5281:
5280:
5273:
5270:
5268:
5265:
5262:
5260:
5241:
5230:
5227:
5225:
5222:
5219:
5217:
5214:
5211:
5209:
5206:
5203:
5201:
5198:
5195:
5193:
5190:
5179:
5172:
5165:
5162:
5160:
5157:
5154:
5152:
5149:
5146:
5143:
5141:
5138:
5131:
5128:
5126:
5119:
5112:
5109:
5103:
5100:
5097:
5093:
5090:
5089:
5088:
5081:
5078:
5076:
5061:
5058:
5056:
5053:
5050:
5048:
5045:
5042:
5040:
5037:
5034:
5032:
5025:
5023:quarto-quartic
5022:
5020:
5017:
5014:
5012:
5005:
5002:
5000:
4993:
4990:
4988:
4985:
4982:
4980:
4977:
4974:
4971:
4967:
4964:
4963:
4962:
4951:
4948:
4946:
4939:
4936:
4934:
4931:Coolidge (1931
4927:
4924:
4922:
4919:
4916:
4914:
4903:
4900:
4898:
4887:
4884:
4882:
4863:
4860:
4858:
4851:
4848:
4846:
4839:
4836:
4834:
4819:
4816:
4814:
4803:
4792:
4789:
4787:
4776:
4773:
4771:
4770:, p. 156–157)
4768:Dolgachev 2012
4764:
4761:
4759:
4756:
4754:
4751:
4749:
4746:
4743:
4740:
4738:
4730:
4727:
4725:
4714:
4695:
4692:
4689:
4686:
4684:
4681:
4678:
4676:
4661:
4655:
4652:
4650:
4647:Dolgachev 2012
4639:
4636:
4633:Julius Plücker
4631:Main article:
4628:
4625:
4623:
4612:
4609:
4607:
4592:
4589:
4587:
4580:
4577:
4575:
4572:
4569:
4567:
4563:
4560:
4558:
4555:
4552:
4550:
4543:
4540:
4538:
4535:
4532:
4530:
4519:
4516:
4514:
4505:is tangent to
4501:orthogonal to
4479:
4476:
4474:
4464:
4461:
4459:
4452:
4449:
4447:
4440:
4437:
4434:
4432:
4429:
4426:
4424:
4413:
4406:
4403:
4399:
4396:
4395:
4394:
4383:
4380:
4378:
4375:
4372:
4370:
4363:
4360:
4358:
4351:
4348:
4346:
4335:
4332:
4330:
4319:
4316:
4305:
4302:
4300:
4289:
4286:
4284:
4281:
4278:
4275:
4273:
4270:
4267:
4263:
4260:
4259:
4258:
4250:
4247:
4245:
4238:
4231:
4224:
4213:
4210:
4208:
4201:
4198:
4196:
4174:singular point
4170:
4167:
4165:
4154:
4151:
4149:
4145:Newton polygon
4143:Main article:
4140:
4138:Newton polygon
4137:
4135:
4128:
4125:
4122:
4120:
4113:
4110:
4108:
4101:
4098:
4094:
4091:
4090:
4089:
4081:
4078:
4076:
4073:
4070:
4068:
4057:
4054:
4052:
4037:
4034:
4032:
4026:
4023:
4021:
4015:
4012:
4010:
3991:
3988:
3985:
3983:
3973:Main article:
3970:
3968:Möbius tetrads
3967:
3965:
3962:
3959:
3957:
3949:
3946:
3942:
3939:
3938:
3937:
3934:
3931:
3929:
3922:
3919:
3917:
3914:
3911:
3909:
3902:
3899:
3897:
3894:
3891:
3889:
3878:
3875:
3873:
3866:
3863:
3861:
3854:Dolgachev 2012
3848:together with
3830:
3827:
3823:
3820:
3819:
3818:
3814:Kummer surface
3812:Main article:
3809:
3807:Kummer surface
3806:
3804:
3797:
3794:
3792:
3781:
3778:
3775:
3770:
3766:
3762:
3759:
3754:
3750:
3746:
3743:
3738:
3734:
3718:
3711:
3707:1.
3705:
3702:
3700:
3693:
3690:
3688:
3682:
3679:
3677:
3662:
3659:
3655:
3652:
3651:
3650:
3647:
3644:
3642:
3635:
3632:
3630:
3623:
3620:
3618:
3611:
3609:Jacobian curve
3608:
3606:
3603:
3596:
3593:
3589:
3586:
3585:
3584:
3549:
3546:
3544:
3533:
3530:
3528:
3509:
3506:
3504:
3493:
3490:
3488:
3477:
3474:
3472:
3469:
3466:
3464:
3461:
3458:
3455:
3452:
3449:
3446:
3443:
3441:
3434:
3427:
3424:
3422:
3415:
3412:
3410:
3402:
3399:
3397:
3394:
3392:
3389:
3386:
3384:
3361:
3358:
3354:
3351:
3350:
3349:
3346:
3343:
3341:
3338:
3335:
3333:
3330:
3327:
3325:
3318:
3315:
3313:
3298:
3295:
3293:
3286:
3283:
3281:
3266:
3263:
3261:
3258:
3256:
3241:
3238:
3236:homology group
3232:
3229:
3227:
3216:
3213:
3210:
3208:
3201:
3194:
3191:
3189:
3186:
3183:homaloidal web
3179:homaloidal net
3163:
3160:
3158:
3151:
3148:
3146:
3143:
3140:
3138:
3131:
3124:
3116:
3113:
3074:
3067:Hessian matrix
3063:
3056:
3053:
3051:
3048:
3046:
3039:
3028:
3025:Dolgachev 2012
3017:
3010:
3003:
2992:
2989:
2985:
2982:
2981:
2980:
2973:
2957:
2954:
2952:
2945:
2942:
2940:
2917:
2914:
2912:
2897:
2894:
2892:
2888:3.
2886:
2881:2.
2879:
2868:
2865:
2863:
2856:
2853:
2850:
2847:
2829:
2828:
2821:
2818:
2816:
2801:
2793:
2782:
2775:
2771:
2768:
2767:
2766:
2763:
2759:
2756:
2753:
2751:
2740:
2737:
2735:
2732:
2729:
2727:
2720:
2717:
2714:
2712:
2705:
2702:
2700:
2689:
2686:
2684:
2677:
2670:
2667:
2665:
2662:
2659:
2657:
2650:
2647:
2645:
2634:
2631:
2629:
2618:
2615:
2612:
2609:
2607:
2604:
2601:
2599:
2592:
2589:
2585:
2582:
2581:
2580:
2565:
2555:
2552:
2550:
2539:
2536:
2534:
2527:
2524:
2522:
2519:
2516:
2514:
2507:equianharmonic
2503:
2500:
2498:equianharmonic
2497:
2495:
2492:
2489:
2487:
2484:
2482:
2472:
2469:
2467:
2460:
2457:
2455:
2452:
2449:
2447:
2444:
2441:
2439:
2428:
2425:
2423:
2416:
2413:
2411:
2408:
2405:
2403:
2392:
2389:
2384:
2381:
2380:
2379:
2360:
2353:
2346:
2343:
2341:
2338:
2335:
2333:
2326:
2323:
2321:
2320:, vol 2, p.3)
2314:
2311:
2308:
2306:
2303:
2300:
2298:
2283:
2280:
2278:
2268:
2265:
2263:
2256:director conic
2248:
2245:
2243:
2240:
2237:
2234:
2231:
2229:
2223:
2216:
2209:
2206:
2199:
2196:
2194:
2187:
2184:
2182:
2175:
2172:
2170:
2167:
2164:
2161:
2159:
2108:
2105:
2102:
2100:
2097:
2094:
2091:
2089:
2086:
2082:
2079:
2078:
2077:
2066:
2063:
2061:
2054:
2051:
2049:
2042:
2039:
2037:
2034:
2031:
2029:
2022:
2019:
2017:
2014:
2011:
2009:
2003:
2000:
1998:
1991:
1988:
1986:
1979:
1976:
1974:
1967:
1966:contravariants
1961:. In practice
1915:
1912:
1910:
1907:
1904:
1902:
1899:
1896:
1894:
1876:
1874:correspondence
1873:
1871:
1864:
1861:
1859:
1851:
1848:
1846:
1843:
1840:
1838:
1837:to covariants.
1832:. In practice
1786:
1783:
1781:
1778:
1775:
1773:
1770:
1767:
1765:
1758:
1751:
1748:
1737:
1734:
1732:
1725:
1722:
1720:
1713:
1710:
1708:
1705:
1702:
1700:
1693:
1690:
1688:
1685:
1678:
1675:
1673:
1670:
1667:
1665:
1660:. In practice
1626:
1623:
1621:
1606:
1603:
1601:
1598:
1595:
1593:
1586:
1583:
1572:
1569:
1567:
1564:complete conic
1560:
1553:
1546:
1539:
1532:
1529:
1527:
1516:
1513:
1511:
1508:
1505:
1503:
1496:
1489:
1486:
1484:
1477:
1474:
1471:
1469:
1466:
1464:
1461:
1450:
1443:
1436:
1433:
1431:
1420:
1417:
1415:
1408:
1401:
1398:
1396:
1389:
1378:
1375:
1373:
1358:
1355:
1353:
1349:
1346:
1344:
1337:
1334:
1332:
1329:
1326:
1324:
1321:
1313:
1298:
1296:characteristic
1295:
1293:
1290:
1288:
1285:
1282:
1279:
1276:
1274:
1271:
1269:
1262:
1259:
1256:Dolgachev 2012
1248:
1239:Main article:
1237:1.
1235:
1229:
1226:
1224:
1221:
1219:
1212:
1209:
1207:
1192:
1189:
1187:
1180:
1173:
1166:
1155:
1148:
1145:
1142:
1138:
1135:
1134:
1133:
1126:
1123:
1121:
1118:
1115:
1113:
1102:
1099:
1097:
1094:Dolgachev 2012
1090:
1087:
1085:
1082:
1075:
1072:
1070:
1067:birational map
1063:
1060:
1057:
1055:
1048:
1045:
1042:
1040:
1033:
1030:
1028:
1021:
1018:
1016:
1013:
1010:
1008:
1002:
999:
997:
994:
991:
989:
985:
976:
973:
971:
964:
961:
959:
948:
945:Dolgachev 2012
917:
914:
911:
909:
902:
899:
896:
894:
891:
888:
886:
883:
880:
878:
871:
868:
866:
855:
852:
850:
839:
832:
829:
825:
822:
821:
820:
817:
814:
812:
804:
801:
799:
796:
794:
791:
788:
786:
783:
780:
778:
767:
764:
762:
759:
756:
754:
747:
744:
742:
735:
732:
730:
725:
722:
720:
713:
710:
708:
705:
702:
700:
697:
694:
692:
689:affine variety
685:
680:1.
678:
675:
673:
642:
639:
637:
626:
623:
621:
614:
611:
609:
604:2.
602:
595:absolute conic
587:absolute plane
583:
580:
578:
571:
568:
566:
559:
552:
549:
545:
542:
541:
540:
524:
521:
518:
515:
512:
509:
506:
495:
488:
486:
483:
480:
478:
458:
455:
452:
449:
446:
443:
440:
429:
426:
422:
419:
418:
417:
414:
410:
406:
399:
396:Kummer surface
375:
374:
373:
366:
363:
356:
348:
335:Dolgachev 2012
324:
322:
319:
314:
313:
308:
303:
298:
293:
288:
283:
278:
273:
268:
263:
258:
253:
248:
243:
238:
233:
228:
223:
218:
213:
208:
203:
198:
193:
188:
183:
178:
172:
166:
164:
148:Coxeter (1969)
87:
86:
41:
39:
32:
9:
6:
4:
3:
2:
7150:
7139:
7136:
7134:
7131:
7129:
7126:
7125:
7123:
7113:
7109:
7105:
7099:
7095:
7091:
7087:
7083:
7079:
7075:
7072:
7068:
7064:
7060:
7056:
7052:
7047:
7042:
7038:
7034:
7033:
7028:
7024:
7020:
7017:
7013:
7009:
7003:
6999:
6995:
6994:Roth, Leonard
6991:
6987:
6984:
6980:
6976:
6972:
6968:
6964:
6960:
6956:
6955:
6950:
6948:
6942:
6938:
6935:
6929:
6925:
6924:
6918:
6915:
6911:
6907:
6901:
6897:
6896:
6891:
6887:
6884:
6878:
6874:
6873:
6868:
6864:
6861:
6857:
6853:
6847:
6843:
6839:
6835:
6831:
6822:on 2014-05-31
6818:
6814:
6808:
6804:
6797:
6796:
6791:
6787:
6784:
6780:
6776:
6770:
6766:
6762:
6758:
6754:
6751:
6747:
6743:
6737:
6733:
6729:
6728:
6723:
6719:
6716:
6712:
6708:
6704:
6700:
6696:
6692:
6688:
6684:
6680:
6679:
6674:
6670:
6667:
6663:
6659:
6655:
6650:
6645:
6641:
6637:
6636:
6631:
6627:
6623:
6619:
6618:
6613:
6609:
6605:
6602:
6598:
6594:
6588:
6584:
6580:
6579:
6573:
6570:
6566:
6562:
6556:
6552:
6548:
6547:
6541:
6538:
6534:
6530:
6524:
6520:
6516:
6515:
6509:
6506:
6502:
6498:
6492:
6488:
6484:
6483:
6477:
6474:
6470:
6466:
6460:
6456:
6452:
6448:
6444:
6443:
6437:
6434:
6430:
6426:
6420:
6416:
6412:
6408:
6404:
6403:
6397:
6396:
6388:
6385:
6383:
6380:
6378:
6375:
6373:
6370:
6368:
6365:
6363:
6360:
6358:
6355:
6353:
6350:
6348:
6345:
6343:
6340:
6339:
6330:
6326:
6320:
6311:
6306:
6301:
6292:
6287:
6278:
6273:
6265:
6261:
6255:
6245:
6236:
6231:
6223:
6219:
6215:
6211:
6207:
6203:
6199:
6188:
6179:
6171:
6163:
6159:
6156:
6152:
6144:
6140:
6137:
6129:
6125:
6121:
6113:
6105:
6101:
6095:
6086:
6082:
6074:
6069:
6061:
6060:twisted cubic
6057:
6049:
6045:
6041:
6037:
6029:
6021:
6017:
6009:
6005:
5997:
5989:
5985:
5977:
5973:
5965:
5957:
5949:
5945:
5937:
5929:
5921:
5913:
5910:
5902:
5898:
5890:
5887:
5879:
5872:
5868:
5860:
5856:
5848:
5844:
5840:
5833:
5829:
5821:
5814:
5810:
5801:
5793:
5789:
5781:
5777:
5769:
5765:
5757:
5753:
5749:
5743:
5734:
5731:
5728:
5725:
5721:
5713:
5709:
5701:
5693:
5689:
5681:
5673:
5665:
5657:
5653:
5649:
5641:
5637:
5634:
5630:
5628:
5627:Salmon (1879)
5624:
5620:
5618:
5617:Jakob Steiner
5614:
5601:
5597:
5589:
5585:
5577:
5573:
5569:
5561:
5553:
5549:
5541:
5533:
5525:
5521:
5517:
5514:of a variety
5513:
5509:
5501:
5493:
5489:
5481:
5478:
5475:
5462:
5458:
5455:
5452:
5439:
5435:
5432:
5428:
5427:Segre variety
5424:
5422:
5421:Corrado Segre
5418:
5414:
5406:
5402:
5394:
5386:
5383:
5379:
5375:
5367:
5366:ruled surface
5363:
5355:
5351:
5348:
5347:Coolidge 1931
5344:
5340:
5336:
5332:
5329:
5324:
5316:
5312:
5304:
5300:
5296:
5292:
5287:
5278:
5277:ruled surface
5274:
5266:
5258:
5254:
5250:
5246:
5242:
5239:
5235:
5231:
5223:
5215:
5207:
5199:
5191:
5188:
5184:
5180:
5177:
5173:
5170:
5166:
5158:
5150:
5147:
5139:
5136:
5132:
5124:
5120:
5117:
5113:
5106:
5101:
5095:
5086:
5082:
5079:quotient ring
5074:
5070:
5066:
5062:
5054:
5046:
5038:
5030:
5026:
5018:
5011:, p.180, 188)
5010:
5006:
4998:
4994:
4986:
4978:
4975:
4969:
4960:
4956:
4952:
4944:
4940:
4932:
4928:
4920:
4912:
4908:
4904:
4896:
4892:
4888:
4880:
4879:Coolidge 1931
4876:
4872:
4868:
4864:
4856:
4852:
4844:
4840:
4832:
4828:
4824:
4820:
4812:
4808:
4804:
4801:
4797:
4793:
4785:
4781:
4777:
4769:
4765:
4747:
4744:
4736:
4731:
4723:
4719:
4715:
4712:
4708:
4704:
4700:
4696:
4693:
4690:
4682:
4674:
4670:
4666:
4662:
4660:
4656:
4648:
4644:
4640:
4637:
4634:
4629:
4621:
4617:
4613:
4605:
4601:
4597:
4593:
4585:
4581:
4573:
4564:
4561:perspectivity
4556:
4548:
4544:
4536:
4528:
4524:
4520:
4512:
4508:
4504:
4500:
4496:
4492:
4488:
4484:
4480:
4473:
4469:
4465:
4457:
4453:
4445:
4444:Coolidge 1931
4441:
4438:
4430:
4422:
4418:
4414:
4411:
4407:
4401:
4392:
4388:
4384:
4376:
4368:
4364:
4356:
4352:
4344:
4340:
4336:
4328:
4324:
4320:
4317:
4314:
4310:
4306:
4298:
4294:
4290:
4282:
4279:
4271:
4265:
4256:
4251:
4248:null-polarity
4243:
4242:normal scheme
4239:
4236:
4232:
4229:
4228:normal bundle
4225:
4222:
4218:
4214:
4206:
4202:
4194:
4190:
4186:
4182:
4178:
4175:
4171:
4163:
4159:
4155:
4146:
4141:
4133:
4129:
4126:
4118:
4117:Coolidge 1931
4114:
4106:
4102:
4096:
4087:
4082:
4074:
4066:
4062:
4058:
4050:
4046:
4042:
4038:
4031:
4027:
4020:
4016:
4008:
4004:
4000:
3996:
3992:
3989:
3981:
3976:
3971:
3963:
3955:
3950:
3944:
3935:
3927:
3923:
3920:linear system
3915:
3907:
3903:
3895:
3887:
3883:
3879:
3871:
3867:
3859:
3858:Coolidge 1931
3855:
3851:
3847:
3843:
3839:
3835:
3831:
3825:
3815:
3810:
3802:
3798:
3779:
3776:
3773:
3768:
3764:
3760:
3757:
3752:
3748:
3744:
3741:
3736:
3732:
3724:is the curve
3723:
3722:Klein quartic
3719:
3716:
3712:
3710:
3706:
3698:
3697:Plücker lines
3694:
3691:Kirkman point
3687:
3686:Salmon (1879)
3683:
3675:
3671:
3667:
3663:
3657:
3648:
3640:
3636:
3628:
3624:
3616:
3612:
3604:
3601:
3597:
3591:
3582:
3578:
3574:
3570:
3566:
3562:
3558:
3554:
3550:
3542:
3538:
3534:
3526:
3522:
3518:
3514:
3510:
3502:
3498:
3494:
3486:
3482:
3478:
3470:
3462:
3459:
3456:
3453:
3450:
3447:
3439:
3435:
3432:
3428:
3420:
3416:
3408:
3403:
3390:
3382:
3378:
3374:
3370:
3366:
3362:
3356:
3347:
3339:
3331:
3323:
3319:
3316:hyperelliptic
3311:
3310:Coolidge 1931
3307:
3303:
3299:
3291:
3287:
3279:
3275:
3271:
3270:Hurwitz curve
3267:
3259:Hurwitz curve
3254:
3250:
3246:
3242:
3239:
3237:
3233:
3225:
3221:
3217:
3214:
3206:
3202:
3199:
3195:
3187:
3184:
3180:
3176:
3175:Coolidge 1931
3172:
3168:
3164:
3156:
3152:
3144:
3136:
3132:
3129:
3125:
3121:
3117:
3114:
3111:
3107:
3103:
3099:
3095:
3091:
3087:
3083:
3079:
3075:
3072:
3068:
3064:
3061:
3057:
3044:
3040:
3037:
3033:
3029:
3026:
3022:
3018:
3015:
3011:
3008:
3004:
3001:
2997:
2993:
2987:
2978:
2974:
2971:
2970:Coolidge 1931
2966:
2962:
2958:
2950:
2946:
2938:
2934:
2930:
2926:
2922:
2918:
2910:
2907:-forms on an
2906:
2902:
2898:
2891:
2887:
2884:
2880:
2877:
2873:
2869:
2861:
2860:generic point
2857:
2854:
2851:
2844:
2841:
2834:
2826:
2822:
2814:
2810:
2806:
2802:
2796:
2785:
2778:
2773:
2764:
2760:
2757:
2749:
2745:
2741:
2733:
2725:
2721:
2718:
2710:
2706:
2698:
2694:
2690:
2682:
2678:
2676:, p. 85, 252)
2675:
2671:
2663:
2655:
2651:
2643:
2639:
2635:
2627:
2626:flat morphism
2623:
2619:
2616:
2613:
2605:
2597:
2593:
2587:
2578:
2574:
2570:
2566:
2564:
2560:
2556:
2548:
2544:
2540:
2532:
2528:
2520:
2512:
2508:
2504:
2501:
2493:
2481:
2480:Salmon (1879)
2477:
2473:
2465:
2461:
2453:
2445:
2437:
2433:
2429:
2421:
2417:
2409:
2401:
2400:cubic surface
2397:
2396:Eckardt point
2393:
2390:Eckardt point
2386:
2377:
2373:
2369:
2365:
2361:
2358:
2354:
2351:
2347:
2339:
2332:configuration
2331:
2327:
2319:
2315:
2312:
2304:
2296:
2292:
2288:
2284:
2277:
2273:
2269:
2261:
2257:
2253:
2249:
2241:
2238:
2235:
2228:
2224:
2221:
2217:
2214:
2210:
2207:
2204:
2200:
2192:
2188:
2185:desmic system
2180:
2176:
2168:
2165:
2157:
2153:
2149:
2145:
2141:
2137:
2133:
2129:
2125:
2121:
2117:
2113:
2109:
2106:
2098:
2095:
2084:
2075:
2071:
2067:
2059:
2055:
2052:cuspidal edge
2047:
2043:
2035:
2027:
2023:
2015:
2007:
2004:
1996:
1992:
1984:
1980:
1972:
1971:Coolidge 1931
1968:
1964:
1960:
1956:
1952:
1948:
1944:
1940:
1936:
1932:
1928:
1924:
1920:
1916:
1908:
1900:
1893:
1889:
1885:
1881:
1877:
1869:
1865:
1857:
1852:
1844:
1835:
1831:
1827:
1823:
1819:
1815:
1811:
1807:
1803:
1799:
1795:
1791:
1787:
1784:contravariant
1779:
1771:
1764:see harmonic.
1763:
1759:
1756:
1752:
1749:
1746:
1742:
1738:
1730:
1726:
1718:
1714:
1706:
1698:
1697:configuration
1694:
1691:configuration
1686:
1683:
1679:
1671:
1663:
1659:
1655:
1651:
1647:
1643:
1639:
1635:
1631:
1627:
1619:
1618:Salmon (1879)
1615:
1611:
1607:
1599:
1591:
1587:
1584:
1581:
1577:
1573:
1565:
1561:
1558:
1554:
1551:
1547:
1544:
1540:
1537:
1533:
1525:
1521:
1517:
1509:
1501:
1500:Coolidge 1931
1497:
1494:
1490:
1482:
1478:
1475:
1462:
1459:
1455:
1451:
1448:
1444:
1441:
1437:
1429:
1428:Salmon (1879)
1425:
1421:
1413:
1409:
1406:
1402:
1399:circumscribed
1394:
1390:
1387:
1383:
1379:
1371:
1370:Coolidge 1931
1367:
1363:
1359:
1350:
1342:
1338:
1330:
1322:
1319:
1318:Coolidge 1931
1314:
1311:
1310:Coolidge 1931
1307:
1303:
1299:
1286:
1283:
1280:
1267:
1263:
1260:
1257:
1253:
1249:
1247:
1246:Salmon (1879)
1242:
1236:
1234:
1233:Arthur Cayley
1230:
1217:
1213:
1206:linear forms.
1205:
1201:
1197:
1196:catalecticant
1193:
1190:catalecticant
1185:
1181:
1178:
1174:
1171:
1167:
1164:
1160:
1159:canonical map
1156:
1153:
1149:
1146:
1140:
1131:
1127:
1119:
1111:
1107:
1103:
1095:
1091:
1083:
1080:
1079:biregular map
1076:
1068:
1064:
1061:
1053:
1049:
1046:
1038:
1034:
1026:
1022:
1014:
1007:
1003:
995:
992:bihomogeneous
988:of a surface.
984:
981:
977:
969:
965:
957:
953:
949:
946:
942:
938:
934:
930:
926:
922:
918:
915:
907:
903:
900:
892:
884:
876:
872:
864:
860:
856:
848:
844:
840:
837:
833:
827:
818:
810:
805:
792:
784:
776:
772:
768:
760:
752:
748:
740:
736:
729:
726:
718:
714:
706:
698:
690:
686:
683:
679:
671:
667:
663:
659:
655:
651:
647:
643:
635:
631:
627:
619:
615:
607:
603:
600:
596:
592:
588:
584:
576:
572:
564:
560:
557:
553:
550:Abelian group
547:
538:
522:
519:
516:
513:
510:
507:
504:
496:
492:
484:
476:
472:
456:
453:
450:
447:
444:
441:
438:
430:
424:
415:
411:
407:
404:
400:
397:
392:
391:
389:
386:
379:
371:
367:
364:
361:
357:
354:
349:
346:
345:
344:
339:
336:
329:
312:
309:
307:
304:
302:
299:
297:
294:
292:
289:
287:
284:
282:
279:
277:
274:
272:
269:
267:
264:
262:
259:
257:
254:
252:
249:
247:
244:
242:
239:
237:
234:
232:
229:
227:
224:
222:
219:
217:
214:
212:
209:
207:
204:
202:
199:
197:
194:
192:
189:
187:
184:
182:
179:
177:
176:Conventions
174:
173:
163:
161:
157:
156:Salmon (1879)
153:
152:Hudson (1990)
149:
145:
141:
137:
133:
129:
125:
121:
117:
112:
110:
106:
102:
98:
94:
93:David Hilbert
83:
80:
72:
62:
58:
52:
51:
45:
40:
31:
30:
27:
19:
7081:
7036:
7030:
6997:
6958:
6952:
6946:
6922:
6894:
6871:
6837:
6824:, retrieved
6817:the original
6794:
6760:
6726:
6682:
6676:
6639:
6633:
6621:
6615:
6577:
6545:
6513:
6481:
6441:
6401:
6217:
6213:
6209:
6205:
6201:
6168:united point
6143:Salmon (1879
6128:Salmon (1879
6106:, p.35, 211)
6008:Salmon (1879
5918:transvectant
5869:Synonym for
5843:tetrahedroid
5837:tetrahedroid
5830:Synonym for
5813:ternary form
5792:tangent cone
5786:tangent cone
5780:Salmon (1879
5762:tacnode-cusp
5656:Salmon (1879
5640:Pascal lines
5600:Salmon (1879
5598:A cusp. See
5576:Salmon (1879
5523:
5519:
5515:
5511:
5381:
5377:
5354:Zariski 1935
5342:
5338:
5334:
5328:Salmon (1879
5309:Salmon conic
5302:
5294:
5290:
5252:
5248:
5247:formed from
5169:irregularity
5135:Coxeter 1969
5105:Salmon (1879
4997:quadrisecant
4991:quadrisecant
4943:Zariski 1935
4917:projectivity
4874:
4870:
4783:
4779:
4721:
4717:
4706:
4702:
4698:
4672:
4664:
4658:
4643:Plücker line
4599:
4582:The line in
4506:
4502:
4498:
4494:
4490:
4486:
4467:
4456:Salmon (1879
4367:Salmon (1879
4342:
4338:
4188:
4187:not zero at
4184:
4180:
4176:
4158:tangent cone
4079:multiplicity
4060:
4044:
4040:
4019:moduli space
4006:
4002:
3998:
3994:
3906:Salmon (1879
3886:Salmon (1879
3870:Salmon (1879
3849:
3845:
3841:
3837:
3833:
3828:Laguerre net
3669:
3665:
3621:Jacobian set
3580:
3576:
3572:
3568:
3564:
3560:
3556:
3552:
3541:Hodge number
3531:irregularity
3501:Salmon (1879
3485:Salmon (1879
3407:Salmon (1879
3376:
3372:
3368:
3364:
3305:
3301:
3290:Salmon (1879
3277:
3273:
3252:
3248:
3244:
3219:
3198:Salmon (1879
3182:
3178:
3120:Hessian pair
3109:
3105:
3101:
3097:
3093:
3089:
3085:
3081:
3077:
3071:Salmon (1879
3058:Named after
3032:harmonic net
3031:
3020:
3006:
2999:
2996:harmonic set
2995:
2964:
2960:
2949:Grassmannian
2943:Grassmannian
2924:
2920:
2908:
2904:
2885:of a surface
2878:of a surface
2862:of a scheme.
2836:
2831:
2812:
2808:
2804:
2794:
2783:
2776:
2699:, p. 85,251)
2695:, p. 116), (
2693:Salmon (1879
2576:
2572:
2568:
2547:Salmon (1879
2531:Salmon (1879
2513:-invariant 0
2510:
2490:equiaffinity
2464:Salmon (1879
2419:
2371:
2367:
2309:double point
2301:double curve
2297:is singular.
2294:
2290:
2286:
2281:discriminant
2255:
2232:differential
2147:
2143:
2139:
2135:
2131:
2127:
2123:
2119:
2115:
2111:
1962:
1958:
1954:
1950:
1946:
1942:
1938:
1934:
1930:
1926:
1922:
1918:
1891:
1887:
1883:
1879:
1868:Salmon (1879
1833:
1829:
1825:
1821:
1817:
1813:
1809:
1805:
1801:
1797:
1793:
1789:
1761:
1661:
1657:
1653:
1649:
1645:
1641:
1637:
1633:
1629:
1576:line complex
1520:collineation
1514:collineation
1453:
1385:
1381:
1365:
1361:
1305:
1252:Cayley octad
1251:
1231:Named after
1203:
1199:
1183:
1176:
1169:
1162:
1158:
1116:bitangential
1110:Salmon (1879
1052:Baker (1922b
1037:Salmon (1879
982:
968:Salmon (1879
956:Salmon (1879
951:
940:
936:
932:
928:
924:
920:
863:Salmon (1879
842:
835:
781:Aronhold set
775:Hodge number
753:, p.55, 231)
739:Salmon (1879
682:Affine space
672:, p.55, 231)
665:
661:
657:
653:
649:
645:
634:Salmon (1879
598:
594:
586:
575:Salmon (1879
490:
427:, , . . . ,
409:explanation.
381:
377:
341:
331:
326:
113:
90:
75:
69:October 2023
66:
47:
26:
6162:unirational
6149:unirational
6104:Salmon 1879
6044:Cayley 1869
5954:tricuspidal
5942:tricircular
5926:transversal
5859:tetrahedron
5853:tetrahedron
5768:Salmon 1879
5756:Cayley 1852
5724:Baker 1922a
5588:Baker 1922a
5572:Cayley 1852
5492:Salmon 1879
5438:Segre cubic
5391:second kind
4933:, p. 224).
4925:propinquity
4849:postulation
4845:, vol 1, )
4843:Baker 1922a
4762:poloquartic
4659:plurigenera
4600:pinch plane
4596:pinch point
4578:perspectrix
4566:perspector.
4541:pentahedron
4511:Salmon 1879
4483:pedal curve
4468:Pascal line
4450:partitivity
4387:Baker 1922b
4355:Cayley 1852
4293:at infinity
4205:Salmon 1879
4193:Cayley 1852
4132:Baker 1922a
3997:of a field
3980:Baker 1922a
3956:, p.14–15)
3709:Felix Klein
3284:hyperbolism
3224:Baker 1922b
3205:Salmon 1879
3192:homographic
3135:Hesse group
3043:Baker 1922b
3036:Baker 1922a
2965:point-group
2807:and degree
2754:fundamental
2654:Cayley 1852
2648:fleflecnode
2642:Salmon 1879
2638:Cayley 1852
2622:flat module
2596:Salmon 1885
2590:facultative
2553:exceptional
2517:equivalence
2476:epitrochoid
2470:epitrochoid
2436:Baker 1922b
2364:dual number
2318:Baker 1922b
2260:Baker 1922b
2197:developable
2156:Salmon 1879
2060:, p.85, 87)
1995:cross-ratio
1989:cross-ratio
1849:correlation
1776:consecutive
1755:Baker 1922b
1745:Salmon 1879
1624:concomitant
1487:coincidence
1481:Baker 1922b
1384:: 0), (1: −
1130:Baker 1922a
1006:binary form
978:The second
843:base number
728:Cross-ratio
618:Baker 1933b
481:∞¹, ∞², ...
337:, p.iii–iv)
321:Conventions
61:introducing
7122:Categories
6826:2012-04-06
6393:References
6134:unipartite
6098:undulation
6026:tritangent
6002:tripartite
5876:third kind
5865:tetrastigm
5678:symmetroid
5658:, p. 352).
5623:Steinerian
5611:Steinerian
5449:self-polar
5384:+1 points.
5330:, p. 127).
5317:, p. 119)
5085:local ring
5035:quaternary
4837:postulated
4722:polar line
4679:point-star
4669:plurigenus
4653:plurigenus
4570:perspector
4466:Short for
4391:Baker 1923
4369:, p. 356).
4291:The curve
4086:local ring
3864:lemniscate
3602:of a curve
3563:such that
3507:involution
3503:, p. 278).
3419:Baker 1923
3400:inflexion
3395:inflection
3344:hyperplane
3211:homography
3161:homaloidal
3060:Otto Hesse
2890:plurigenus
2602:first kind
2533:, p. 184).
2485:equiaffine
2357:dual curve
2324:double six
2154:, p.30), (
2103:deficiency
2020:cubo-cubic
1897:cosingular
1862:coresidual
1711:congruence
1668:concurrent
1112:, p. 328).
1058:birational
1043:bipunctual
980:plurigenus
962:biflecnode
897:bielliptic
881:bicuspidal
853:bicircular
836:base point
789:associated
612:accidental
577:, p. 356).
362:, p.20–21)
311:References
101:André Weil
44:references
7071:186210189
7055:0080-4614
6983:119948968
6975:0025-5831
6892:(1879) ,
6715:109359205
6699:0080-4614
6658:0080-4614
6139:Connected
6130:, p. 29).
6118:unicursal
6110:unibranch
6014:trisecant
5978:, p.152)
5970:trihedral
5903:, p.204).
5884:threefold
5826:tetragram
5706:syzygetic
5570:A cusp. (
5463:, p.123)
5321:satellite
5234:resultant
5228:resultant
4937:proximate
4881:, p.176)
4774:polygonal
4757:polocubic
4752:poloconic
4649:, p.124)
4458:, p.165).
4446:, p.192)
4207:, p. 207)
4199:node cusp
3860:, p. 423)
3660:kenotheme
3487:, p.103).
3481:inversion
3475:inversion
3467:invariant
3425:inscribed
3383:, p.381)
3328:hyperflex
3296:hypercusp
3292:, p.175).
3200:, p.232).
3173:, p.45) (
3027:, 3.1.2)
2935:, p.45) (
2819:generator
2598:, p.243)
2549:, p. 40).
2466:, p. 65).
2450:enneaedro
2406:effective
2266:directrix
2173:Desargues
2130:–2)/2 – (
1913:covariant
1735:conjugate
1596:composite
1506:collinear
1502:, p. 126)
1320:, p.220)
1291:character
1258:, 6.3.1)
1143:canonical
1106:bitangent
1100:bitangent
1088:biscribed
1073:biregular
1039:, p.165).
1031:bipartite
970:, p.210).
958:, p.223).
921:bifid map
865:, p.231).
741:, p.119).
733:antipoint
703:aggregate
569:aberrancy
517:…
451:…
7080:(1935),
7025:(1853),
6996:(1949),
6943:(1886),
6869:(1916),
6836:(1990),
6792:(2012),
6759:(1969),
6724:(1931),
6610:(1852),
6336:See also
6266:, p.160)
6224:, p.368)
6145:, p.165)
6124:rational
6087:, p.193)
6010:, p.165)
5994:trinodal
5962:trigonal
5782:, p.76).
5770:, p.207)
5686:syntheme
5652:Cayleyan
5602:, p.23).
5530:singular
5494:, p.132)
5472:septimic
5399:secundum
5259:, p.180)
5220:residual
5171:is zero.
5144:rational
5137:, p.242)
5107:, p.46)
5098:ramphoid
5065:quippian
5059:quippian
5031:, p.187)
4945:, p.9).
4857:, p.440)
4817:poristic
4728:polarity
4626:Plücker
4620:Cayleyan
4606:, p.175)
4435:parallel
4361:osculate
4333:ordinary
4315:, p.15)
4071:multiple
4067:, p.187)
4051:, p.187)
3947:manifold
3916:Degree 1
3680:keratoid
3641:, p.117)
3629:, p.119)
3617:, p.115)
3594:Jacobian
3547:isologue
3497:involute
3491:involute
3444:integral
3409:, p. 32)
3312:, p. 18)
3230:homology
3207:, p.283)
3149:homaloid
3073:, p.55).
2990:harmonic
2939:, p.159)
2842:, p.iii)
2762:defined.
2750:, p.26).
2711:, p.422)
2683:, p.252)
2644:, p.210)
2632:flecnode
2525:evectant
2458:envelope
2442:embedded
2378:, p.268)
2246:director
2205:, p.85).
2158:, p. 28)
2122:–2)/2 –(
2076:, p.141)
2028:, p.179)
1973:, p.151)
1945:, where
1870:, p.131)
1841:coplanar
1816:, where
1703:confocal
1644:, where
1610:conchoid
1604:conchoid
1543:complete
1538:, p.351)
1530:complete
1376:circular
1372:, p. 50)
1312:, p.99)
1241:Cayleyan
1227:Cayleyan
1027:, p.424)
947:, p.215)
889:bidegree
815:azygetic
745:apparent
695:affinity
636:, p.23).
581:absolute
539:, p.288)
471:Schubert
387:, p.iii)
306:See also
95:and the
7112:1336146
7016:0814690
6914:0115124
6860:1097176
6783:0123930
6750:0120551
6601:2850141
6569:2850139
6537:2849669
6505:2857520
6473:2857757
6433:2849917
6242:virtual
6196:valency
6191:valence
6157:, p.20)
6054:twisted
5807:ternary
5752:tacnode
5746:tacnode
5662:surface
5606:Steiner
5578:, p.23)
5566:spinode
5263:reverse
5204:related
5196:regulus
5163:regular
5118:, p.84)
5051:quintic
5043:quartic
5015:quantic
4983:quadric
4961:, p.15)
4913:, p.10)
4713:, p.11)
4657:Plural
4610:pippian
4513:, p.96)
4349:oscnode
4329:, p.46)
4287:ombilic
4237:, p.16)
4164:, p.26)
4013:modulus
3908:, p. 7)
3888:, p.43)
3882:limaçon
3876:limaçon
3872:, p.42)
3054:Hessian
2874:or the
2848:generic
2738:freedom
2543:evolute
2537:evolute
2414:elation
2274:or the
2092:decimic
2070:cyclide
2064:cyclide
2006:Crunode
2001:crunode
1937:⊕
1808:⊕
1747:, p.23)
1684:, p.18)
1636:⊕
1632:⊕
1614:cissoid
1570:complex
1472:coaxial
1460:, p.28)
1449:, p.85)
1442:, p.28)
1424:cissoid
1418:cissoid
1356:circuit
1216:caustic
1210:caustic
1011:binodal
974:bigenus
711:ambient
640:adjoint
473: (
421:Symbols
57:improve
7110:
7100:
7069:
7063:108572
7061:
7053:
7014:
7004:
6981:
6973:
6930:
6912:
6902:
6879:
6858:
6848:
6809:
6781:
6771:
6748:
6738:
6713:
6707:108996
6705:
6697:
6666:108626
6664:
6656:
6599:
6589:
6567:
6557:
6535:
6525:
6503:
6493:
6471:
6461:
6431:
6421:
6141:. See
5818:tetrad
5803:curve.
5718:syzygy
5698:system
5654:. See
5554:, p.4)
5506:simple
5498:sextic
5467:septic
5407:, p.2)
5372:secant
5360:scroll
4901:primal
4897:, p.1)
4796:porism
4790:porism
4737:, p.9)
4553:period
4533:pentad
4517:pencil
4462:Pascal
4404:Pappus
4297:sphere
4257:, p.9)
4211:normal
4035:monoid
3912:linear
3832:A net
3523:, and
3253:center
2162:degree
1905:couple
1890:×
1858:, p.7)
1768:connex
1741:acnode
1495:, p.8)
1467:coaxal
1347:circle
1277:centre
1272:center
1222:Cayley
1019:binode
1000:binary
935:of 2+2
875:bicorn
869:bicorn
861:. See
757:apolar
707:A set.
676:affine
630:acnode
624:acnode
46:, but
7067:S2CID
7059:JSTOR
6979:S2CID
6945:"Die
6820:(PDF)
6799:(PDF)
6711:S2CID
6703:JSTOR
6662:JSTOR
6624:: 166
6176:unode
6066:total
6040:trope
6034:trope
5934:triad
5907:torse
5546:solid
5411:Segre
5271:ruled
5129:range
4885:prime
4718:polar
4687:polar
4602:. (
4590:pinch
4477:pedal
4385:See (
4303:order
4276:octic
4268:octad
4152:nodal
4047:–1. (
3986:model
3932:locus
3703:Klein
3417:See (
3308:+1. (
3141:hexad
3049:Hesse
2977:group
2961:group
2955:group
2915:grade
2866:genus
2707:See (
2687:focus
2668:focal
2087:decic
2032:curve
2012:cubic
1729:conic
1723:conic
1434:class
1327:chord
912:bifid
797:axial
140:1933b
136:1933a
124:1922b
120:1922a
7098:ISBN
7051:ISSN
7002:ISBN
6971:ISSN
6928:ISBN
6900:ISBN
6877:ISBN
6846:ISBN
6807:ISBN
6769:ISBN
6736:ISBN
6695:ISSN
6654:ISSN
6587:ISBN
6555:ISBN
6523:ISBN
6491:ISBN
6459:ISBN
6419:ISBN
6327:The
6079:type
5582:star
5538:skew
5337:–1)(
5110:rank
5069:1857
4949:pure
4829:and
4741:pole
4701:–1,
4663:The
4616:1857
4525:and
4481:The
4168:node
4111:nest
4103:The
4028:See
3960:meet
3892:line
3799:The
3674:1853
3645:join
3535:The
3245:axis
2899:The
2715:form
2660:flex
2640:). (
2610:flat
2430:The
2420:axis
2387:env
2344:dual
2336:duad
2328:The
2250:The
2134:–1)(
2126:–1)(
2118:–1)(
2046:cusp
2040:cusp
1993:The
1953:and
1866:See
1824:and
1676:cone
1652:and
1362:even
1244:See
943:}. (
830:base
802:axis
769:The
475:1886
181:!$ @
132:1925
128:1923
116:2012
107:and
7090:doi
7041:doi
7037:143
6963:doi
6687:doi
6683:159
6644:doi
6640:147
6451:doi
6411:doi
6317:XYZ
6258:web
5574:),
5429:or
5419:or
5155:ray
4957:. (
4909:. (
4893:. (
4809:or
4720:or
4667:th
4509:. (
4485:of
4191:. (
4160:. (
4123:net
3495:An
3479:An
3379:).
3371:or
3181:or
3169:. (
2963:or
2789:, γ
2746:. (
2541:An
2474:An
2394:An
2289:in
1882:to
1743:. (
1366:odd
1364:or
1161:or
715:An
644:If
628:An
597:or
535:. (
301:XYZ
142:),
7124::
7108:MR
7106:,
7096:,
7088:,
7065:,
7057:,
7049:,
7035:,
7029:,
7012:MR
7010:,
6992:;
6977:,
6969:,
6959:26
6957:,
6951:,
6910:MR
6908:,
6856:MR
6854:,
6844:,
6805:,
6801:,
6779:MR
6777:,
6767:,
6746:MR
6744:,
6734:,
6730:,
6709:,
6701:,
6693:,
6681:,
6660:,
6652:,
6638:,
6620:,
6614:,
6597:MR
6595:,
6585:,
6565:MR
6563:,
6553:,
6533:MR
6531:,
6521:,
6501:MR
6499:,
6489:,
6469:MR
6467:,
6457:,
6449:,
6429:MR
6427:,
6417:,
6409:,
6218:kP
6216:)+
6058:A
6038:A
5946:A
5841:A
5790:A
5750:A
5364:A
5185:,
5063:A
4995:A
4594:A
4503:PX
4172:A
3924:A
3880:A
3780:0.
3571:,
3567:,
3519:,
3320:A
3268:A
3112:.
3110:AB
3108:,
3106:CA
3104:,
3102:BC
3096:,
3092:,
3084:,
3080:,
2972:)
2947:A
2656:).
2624:,
2561:,
2370:+ε
2146:.
2068:A
2044:A
1981:A
1947:SV
1935:SV
1929:,
1921:,
1818:SV
1806:SV
1800:,
1792:,
1727:A
1695:A
1646:SV
1630:SV
1608:A
1518:A
1422:A
1339:A
1214:A
1194:A
1104:A
873:A
593:,
493:}
477:).
162:.
158:,
154:,
150:,
146:,
138:,
134:,
130:,
126:,
122:,
103:,
7092::
7043::
6965::
6947:n
6689::
6646::
6622:7
6453::
6413::
6312:.
6252:W
6214:P
6212:(
6210:T
6206:k
6202:T
6185:V
6092:U
6075:)
6071:(
6022:.
5990:.
5914:.
5849:.
5758:)
5740:T
5714:.
5694:)
5526:.
5524:V
5520:W
5516:V
5512:W
5382:n
5378:n
5343:n
5339:n
5335:n
5305:.
5303:n
5295:n
5291:S
5284:S
5253:n
5249:n
5189:.
5178:.
5092:R
4966:Q
4875:n
4871:n
4784:k
4780:k
4733:(
4707:n
4703:n
4699:n
4673:d
4665:d
4529:.
4507:C
4499:X
4495:X
4491:P
4487:C
4423:.
4412:.
4398:P
4357:)
4343:m
4339:m
4262:O
4253:(
4244:.
4230:.
4223:.
4195:)
4189:p
4185:f
4181:f
4177:p
4119:)
4093:N
4061:n
4045:n
4041:n
4007:K
4003:k
3999:k
3995:K
3941:M
3850:d
3846:V
3842:V
3838:d
3834:V
3822:L
3777:=
3774:x
3769:3
3765:z
3761:+
3758:z
3753:3
3749:y
3745:+
3742:y
3737:3
3733:x
3670:n
3666:n
3654:K
3588:J
3581:p
3577:x
3575:(
3573:T
3569:x
3565:p
3561:x
3557:p
3553:T
3543:.
3527:.
3440:.
3433:.
3377:D
3375:(
3373:i
3369:i
3365:D
3353:I
3306:r
3302:r
3278:g
3274:g
3255:.
3185:.
3157:.
3098:C
3094:B
3090:A
3086:C
3082:B
3078:A
3062:.
3007:j
2984:H
2968:(
2925:n
2921:n
2909:n
2905:n
2838:(
2813:g
2809:d
2805:r
2795:d
2784:d
2777:g
2770:G
2726:.
2628:.
2584:F
2511:j
2402:.
2383:E
2372:b
2368:a
2295:P
2291:n
2287:d
2193:.
2181:.
2148:b
2144:a
2140:n
2136:b
2132:b
2128:a
2124:a
2120:n
2116:n
2112:D
2081:D
1963:V
1959:V
1955:V
1951:V
1943:V
1939:V
1931:y
1927:x
1923:y
1919:x
1892:Y
1888:X
1884:Y
1880:X
1854:(
1834:V
1830:V
1826:V
1822:V
1814:V
1810:V
1802:y
1798:x
1794:y
1790:x
1662:V
1658:V
1654:V
1650:V
1642:V
1638:V
1634:V
1620:.
1592:.
1454:r
1430:.
1414:.
1407:.
1386:i
1382:i
1316:(
1204:n
1200:n
1137:C
1096:)
986:2
983:P
941:S
937:g
933:S
929:g
925:g
908:.
849:.
824:B
807:(
777:.
666:C
662:r
658:r
654:C
650:C
646:C
565:.
558:.
544:A
523:n
520:,
514:,
511:2
508:,
505:1
491:n
457:n
454:,
448:,
445:2
442:,
439:1
383:(
333:(
296:W
291:V
286:U
281:T
276:S
271:R
266:Q
261:P
256:O
251:N
246:M
241:L
236:K
231:J
226:I
221:H
216:G
211:F
206:E
201:D
196:C
191:B
186:A
82:)
76:(
71:)
67:(
53:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.