119:'s theory in the 1980s. Iskovskikh obtained a complete classification of minimal rational surfaces over arbitrary fields and studied the groups of birational automorphisms for all classes of birational surfaces over any perfect field. He is the author or coauthor of more than 80 scientific publications, including 2 monographs. His PhD students include
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Much of the modern development of birational geometry began with
Iskovskikh and Manin's Β«Π’ΡΠ΅Ρ
ΠΌΠ΅ΡΠ½ΡΠ΅ ΠΊΠ²Π°ΡΡΠΈΠΊΠΈ ΠΈ ΠΊΠΎΠ½ΡΡΠΏΡΠΈΠΌΠ΅ΡΡ ΠΊ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ΅ ΠΡΡΠΎΡΠ°Β» (ΠΠ°ΡΠ΅ΠΌ. ΡΠ±., 1971, Ρ. 86, No. 1) (Three-dimensional quartics and counterexamples to the LurΓΆth problem) (Mat. Sb., 1971, vol. 86, no. 1, pp. 140β166). In
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All of
Iskovskikh's research is connected with Shafarevich's Moscow school of algebraic geometry. Shafarevich's school included the construction of a systematic theory of algebraic surfaces, including the theory of rational surfaces with rich birational geometry. Continuing the fundamental research
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and from 1974 to 1977 at the All-Russian
Research Institute of Integrated Automation of the Oil and Gas Industry. In the Department of Higher Algebra of Moscow State University's Faculty of Mechanics and Mathematics, he was from 1977 to 1987 a senior researcher, from 1987 to 1990 a leading
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it, an effective method (the "method of maximal singularities") is constructed, which allows one to comprehensively describe birational maps of rationally connected three-dimensional manifolds. The three-dimensional quartic is foundational for modern research in birational geometry.
108:. The theorems provided general principles for birational classification in dimension three. Iskovskikh and Manin's research made three-dimensional birational geometry into a systematic theory.
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73:. After graduating in 1964, Iskovskikh entered the graduate school of the Faculty of Mechanics and Mathematics of Moscow State University and received in 1968 his
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From June 29 to July 3, 2009, the
Steklov Institute held an international conference on the geometry of algebraic varieties as a memorial to V. A. Iskovskikh.
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of Yuri Manin, Iskovskikh obtained the first important results on the birational type of rational surfaces; the results were published in his PhD thesis.
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In the 1970s
Iskovskikh applied the method of maximal singularities to prove important theorems on birational maps of several classes of
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206:(Russian), Parts 1 & 2, Mat. USSR Izv., vol. 11, 1977, pp. 485β527, vol. 12, 1978, pp. 469β506;
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185:: Π’ΡΠ΅Ρ
ΠΌΠ΅ΡΠ½ΡΠ΅ ΠΊΠ²Π°ΡΡΠΈΠΊΠΈ ΠΈ ΠΊΠΎΠ½ΡΡΠΏΡΠΈΠΌΠ΅ΡΡ ΠΊ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ΅ ΠΡΡΠΎΡΠ°, Mat. Sbornik, vol. 86, 1971, pp. 140β166
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Iskovskikh, V. A. (1984). "Algebraic threefolds with special regard to the problem of rationality".
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researcher, and from 1990 until his death a professor. In the
Department of Number Theory of the
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Iskovskikh worked from 1968 to 1974 at the
Central Economics and Mathematics Institute of the
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Born into a peasant family, Iskovskikh entered in 1958 the
Physics and Mathematics Faculty of
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45:β 4 January 2009, Moscow) was a Russian mathematician, specializing in algebraic geometry.
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Pukhlikov, Aleksandr V. (1998). "Essentials of the method of maximal singularities".
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Algebraic 3-folds with special regard to the problem of rationality
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in Warsaw. In 2000 he was awarded the A.A. Markov Prize of the
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Algebraic
Geometry II, Encyclopedia of Mathematical Sciences
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Academic staff of the
Steklov Institute of Mathematics
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Encyclopedia of Mathematical Sciences, Springer, 1999
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In 1983 Iskovskikh was an Invited Speaker with talk
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280:Beauville, Arnaud (2015). "The LΓΌroth problem".
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, 1 July 1939,
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ΠΠ°ΡΠΈΠ»ΠΈΠΉ ΠΠ»Π΅ΠΊΡΠ΅Π΅Π²ΠΈΡ (1939β2009)"
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ΠΠ°ΡΠΈΠ»ΠΈΡ ΠΠ»Π΅ΠΊΡΠ΅Π΅Π²ΠΈΡΠ°"
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129:Dmitri Olegovich Orlov
39:Alekseevich Iskovskikh
198:Algebraic Geometry V.
161:Selected publications
75:Candidate of Sciences
49:Education and career
456:Algebraic geometers
148:University of Turin
71:birational geometry
327:Vasilii Iskovskikh
172:Algebraic Surfaces
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