192:#include "colors.inc" #include "stdinc.inc" background { Blue } camera { location <0,-12,6> up z right x look_at <0,0,0> } light_source {<120,0,120> rgb <1.0, 1.0, 1.0>} light_source {<-120,-120,0> rgb <0.8, 1.0, 1.0>*0.5} #declare my_texture = texture { pigment { rgb <0.8,0.8,1> } finish { phong 0.5 phong_size 10 } } #declare w = 1; #declare T = function { 64*(x-w)*( pow(x,4) -4*pow(x,3)*w -10*x*x*y*y -4*x*x*w*w +16*x*pow(w,3) -20*x*y*y*w+ 5*pow(y,4) +16*pow(w,4) -20*y*y*w*w) -5*sqrt(5-sqrt(5))*(2*z-sqrt(5-sqrt(5))*w) * pow(4*(x*x+y*y-z*z)+(1+3*sqrt(5))*w*w,2) } isosurface { function { T(x,y,z) } threshold 0 accuracy 0.0001 max_gradient 2000000 open contained_by {sphere {<0,0,0>,6}} texture{ my_texture } }
396:"}},"text\/plain":{"en":{"":"author name string"}}},"{\"value\":\"Claudio Rocchini\",\"type\":\"string\"}":{"text\/html":{"en":{"P2093":"Claudio Rocchini"}},"text\/plain":{"en":{"P2093":"Claudio Rocchini"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":4174,\"id\":\"P4174\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":"
388:
300:
215:
220:
82:
547:"}},"text\/plain":{"en":{"P275":"GNU Free Documentation License, version 1.2 or later"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":14946043,\"id\":\"Q14946043\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"P275":"
543:"}},"text\/plain":{"en":{"":"copyright license"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":50829104,\"id\":\"Q50829104\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"P275":"
499:"}},"text\/plain":{"en":{"":"copyright status"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":50423863,\"id\":\"Q50423863\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"P6216":"
608:"}},"text\/plain":{"en":{"":"source of file"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":66458942,\"id\":\"Q66458942\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"P7482":"
404:"}},"text\/plain":{"en":{"P4174":"Rocchini"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":2699,\"id\":\"P2699\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":"
392:"}},"text\/plain":{"en":{"":"creator"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":2093,\"id\":\"P2093\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":"
604:
1524:
408:"}},"text\/plain":{"en":{"":"URL"}}},"{\"value\":\"http:\\\/\\\/commons.wikimedia.org\\\/wiki\\\/User:Rocchini\",\"type\":\"string\"}":{"text\/html":{"en":{"P2699":"
690:
400:"}},"text\/plain":{"en":{"":"Wikimedia username"}}},"{\"value\":\"Rocchini\",\"type\":\"string\"}":{"text\/html":{"en":{"P4174":"
1344:
261:– You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
401:
1379:
1569:
1464:
1449:
609:
548:
544:
500:
409:
605:
496:
405:
397:
393:
540:
389:
317:
1314:
1259:
1064:
1231:
722:
1469:
1369:
924:
551:"}},"text\/plain":{"en":{"P275":"Creative Commons Attribution-ShareAlike 3.0 Unported"}}}}": -->
412:"}},"text\/plain":{"en":{"P2699":"http:\/\/commons.wikimedia.org\/wiki\/User:Rocchini"}}}}": -->
1319:
1414:
1404:
315:; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled
166:
1074:
1578:
1454:
1439:
839:
1374:
635:
591:
574:
526:
1399:
1214:
1284:
809:
1364:
268:
707:{{Information |Description={{en|1=Togliatti Surface with w=1, bounded by a sphere with radius=6}} |Source={{own}} |Author=
854:
52:
48:
42:
619:
510:
474:
459:
446:
764:
612:"}},"text\/plain":{"en":{"P7482":"original creation by uploader"}}}}": -->
307:
93:
1389:
558:
419:
378:
61:
1434:
864:
466:
230:
1104:
894:
1194:
989:
879:
789:
721:
More than 100 pages use this file. The following list shows the first 100 pages that use this file only. A
312:
1459:
1424:
1394:
1384:
1349:
1249:
1224:
1099:
1044:
944:
824:
267:– If you remix, transform, or build upon the material, you must distribute your contributions under the
1419:
1149:
1039:
799:
739:
503:"}},"text\/plain":{"en":{"P6216":"copyrighted"}}}}": -->
1339:
1089:
1004:
1029:
979:
774:
101:
914:
1129:
1124:
1094:
934:
1429:
994:
969:
929:
481:
305:
Permission is granted to copy, distribute and/or modify this document under the terms of the
904:
1189:
1079:
784:
227:
1109:
8:
1204:
1199:
1179:
1119:
899:
869:
859:
759:
1409:
1354:
1024:
984:
954:
754:
749:
689:
684:
37:
1184:
919:
1359:
1159:
1139:
1014:
814:
779:
202:
I, the copyright holder of this work, hereby publish it under the following licenses:
88:
368:
1219:
1049:
1009:
974:
909:
1164:
1059:
1054:
1034:
964:
949:
939:
844:
829:
819:
794:
734:
1169:
1114:
884:
769:
155:
1209:
1174:
1069:
1019:
959:
708:
700:
1154:
1144:
999:
889:
874:
804:
1489:
629:
585:
568:
520:
429:
1534:
1514:
1549:
1494:
1304:
1134:
849:
1444:
1329:
1559:
294:
1084:
834:
657:
Click on a date/time to view the file as it appeared at that time.
186:
1294:
1269:
1544:
1504:
744:
729:
1274:
1484:
136:
Togliatti
Surface with w=1, bounded by a sphere with radius=6
76:
1539:
1479:
719:
1240:
655:
592:
Creative
Commons Attribution-ShareAlike 3.0 Unported
575:
549:
Creative
Commons Attribution-ShareAlike 3.0 Unported
545:
311:, Version 1.2 or any later version published by the
100:
Commons is a freely licensed media file repository.
410:
http:\/\/commons.wikimedia.org\/wiki\/User:Rocchini
1065:Noether's theorem on rationality for surfaces
711:|Date= |Permission=cc-by-3.0 |other_versions= }}
66:(800 × 800 pixels, file size: 163 KB, MIME type:
278:https://creativecommons.org/licenses/by-sa/3.0
81:
284:Creative Commons Attribution-Share Alike 3.0
208:
161:
123:
151:
141:
14:
244:– to copy, distribute and transmit the work
482:http://commons.wikimedia.org/User:Rocchini
343:You may select the license of your choice.
1242:The following other wikis use this file:
925:Grauert–Riemenschneider vanishing theorem
1465:کاربر:Mojtabakd/جعبههای کاربری/wrapper
1215:Weber's theorem (Algebraic curves)
112:
323:http://www.gnu.org/copyleft/fdl.html
231:Attribution-Share Alike 3.0 Unported
855:Cylindrical algebraic decomposition
648:
219:
214:
13:
1470:کاربر:Iran.amir.mohammad/درباره من
765:Arithmetic and geometric Frobenius
367:
361:
342:
205:
201:
130:
113:
59:
1590:
810:Brieskorn–Grothendieck resolution
366:
840:Chevalley–Iwahori–Nagata theorem
352:
299:
298:
255:Under the following conditions:
226:This file is licensed under the
218:
213:
207:
80:
31:
21:
1345:ویکیپدیا:الگوهای کاربر/ریاضیات
1075:Néron–Ogg–Shafarevich criterion
865:Differential algebraic geometry
349:
131:
1237:
652:
348:
329:GNU Free Documentation License
318:GNU Free Documentation License
308:GNU Free Documentation License
180:
26:
1:
1525:အက္ခရာသင်္ချာနည်းကျ ဂျီဩမေတြီ
1490:Templat:Aljabar-geometri-stub
1105:Regular semi-algebraic system
636:original creation by uploader
610:original creation by uploader
1195:Universal algebraic geometry
716:
374:Items portrayed in this file
195:
7:
1380:کاربر:جعبه کاربر/هندسه جبری
1281:Usage on ckb.wikipedia.org
1150:Tate's isogeny theorem
1100:Ramanujam vanishing theorem
990:Lamé's special quartic
825:Butterfly curve (algebraic)
189:. This is the source code:
10:
1595:
1566:Usage on ru.wikipedia.org
1556:Usage on pt.wikipedia.org
1550:Gebruiker:Woutput/Kladblok
1531:Usage on nl.wikipedia.org
1521:Usage on my.wikipedia.org
1511:Usage on ja.wikipedia.org
1501:Usage on it.wikipedia.org
1476:Usage on id.wikipedia.org
1336:Usage on fa.wikipedia.org
1326:Usage on es.wikipedia.org
1311:Usage on el.wikipedia.org
1305:Eugenio Giuseppe Togliatti
1301:Usage on de.wikipedia.org
1291:Usage on cy.wikipedia.org
1266:Usage on ca.wikipedia.org
1256:Usage on ba.wikipedia.org
1246:Usage on ar.wikipedia.org
269:same or compatible license
120:
115:
1320:Συζήτηση χρήστη:Nafsika08
1040:Mumford vanishing theorem
895:Fourier–Deligne transform
800:Borel fixed-point theorem
649:
145:
16:
1570:Алгебраическая геометрия
1450:ریخت بین واریتههای جبری
1090:Periodic table of shapes
1005:Locally acyclic morphism
915:Giambelli's formula
880:Enriques–Babbage theorem
790:Bombieri–Lang conjecture
351:
313:Free Software Foundation
235:
87:This is a file from the
36:
1375:کاربر:Mojtabakd/اطلاعات
1225:Zeuthen–Segre invariant
1045:Nagata–Biran conjecture
1030:Multiplicative distance
995:Lange's conjecture
980:Kempf vanishing theorem
945:Horrocks–Mumford bundle
706:
91:. Information from its
1535:Algebraïsche meetkunde
1130:Shioda modular surface
94:description page there
41:Size of this preview:
1110:Reider's theorem
1095:Plücker's conoid
970:Intermediate Jacobian
740:Abhyankar–Moh theorem
126:Togliatti surface.png
1330:Geometría algebraica
1295:Geometreg algebraidd
1270:Geometria algebraica
1190:Unibranch local ring
1080:Ordinary singularity
785:Bogomolov conjecture
1560:Geometria algébrica
1545:Togliatti-oppervlak
1505:Geometria algebrica
1370:الگو:هندسه جبری-خرد
1315:Αλγεβρική γεωμετρία
1260:Алгебраик геометрия
1205:Virasoro conjecture
1200:Valuative criterion
1185:Tsen's theorem
1180:Tschirnhausen cubic
1120:Semialgebraic space
920:Gram's theorem
900:Frobenius splitting
870:Du Bois singularity
860:De Franchis theorem
775:Barth–Nieto quintic
760:Alternating algebra
250:– to adapt the work
47:Other resolutions:
1495:Aljabar Calabi–Yau
1125:Serre–Tate theorem
1025:Moishezon manifold
985:Kuga fiber variety
955:Hyperplane section
935:Honda–Tate theorem
905:Fröberg conjecture
755:Algebraic manifold
750:Algebraic geometry
685:09:15, 1 July 2010
460:Wikimedia username
447:author name string
398:Wikimedia username
394:author name string
1579:more global usage
1415:گروه تیت-شافارویچ
1275:Eugenio Togliatti
1238:Global file usage
1160:Togliatti surface
1140:Symmetric variety
1015:Manin obstruction
930:Hodge–Tate module
815:Bullet-nose curve
780:Beauville surface
714:
559:copyright license
541:copyright license
362:Togliatti Surface
360:
340:
339:
177:
176:
170:
167:Reusing this file
109:
108:
89:Wikimedia Commons
32:Global file usage
1586:
1485:Geometri aljabar
1405:توپولوژی زاریسکی
1220:Wirtinger sextic
1050:Nakai conjecture
1010:Logarithmic pair
975:Irrelevant ideal
910:General elephant
709:Claudio Rocchini
697:
659:
511:copyright status
497:copyright status
484:
479:
469:
464:
454:
453:Claudio Rocchini
451:
358:
336:
333:
330:
327:
324:
302:
301:
295:
291:
288:
285:
282:
279:
271:as the original.
228:Creative Commons
222:
221:
217:
216:
211:
210:
164:
156:Claudio Rocchini
147:
135:
127:
121:
105:
84:
83:
77:
71:
69:
56:
53:480 × 480 pixels
49:240 × 240 pixels
43:600 × 600 pixels
1594:
1593:
1589:
1588:
1587:
1585:
1584:
1583:
1455:تحلیل تکینگیها
1440:فرمول گونا–درجه
1360:کاربر:Mojtabakd
1236:
1165:Torelli theorem
1060:Newton polytope
1055:Nash blowing-up
1035:Mumford measure
965:Imaginary curve
950:Humbert surface
940:Horrocks bundle
845:Chordal variety
830:Cartan subgroup
820:Burniat surface
795:Bordiga surface
735:Abelian surface
715:
703:
695:
651:
650:
647:
646:
645:
644:
643:
642:
641:
640:
638:
626:
625:
624:
622:
603:
602:
601:
600:
599:
598:
597:
596:
594:
583:
582:
581:
580:
579:
577:
565:
564:
563:
561:
538:
537:
536:
535:
534:
533:
532:
531:
529:
517:
516:
515:
513:
494:
493:
492:
491:
490:
489:
488:
487:
486:
485:
480:
477:
471:
470:
465:
462:
456:
455:
452:
449:
440:
439:
438:
436:
426:
425:
424:
422:
387:
386:
385:
384:
383:
381:
365:
364:
363:
346:
345:
344:
334:
331:
328:
325:
322:
293:
292:
289:
286:
283:
280:
277:
276:
234:
223:
204:
203:
198:
193:
185:Many thanks to
183:
178:
137:
125:
118:
111:
110:
99:
98:
97:is shown below.
73:
67:
65:
58:
57:
46:
12:
11:
5:
1592:
1581:of this file.
1575:
1574:
1573:
1572:
1564:
1563:
1562:
1554:
1553:
1552:
1547:
1542:
1537:
1529:
1528:
1527:
1519:
1518:
1517:
1509:
1508:
1507:
1499:
1498:
1497:
1492:
1487:
1482:
1474:
1473:
1472:
1467:
1462:
1457:
1452:
1447:
1442:
1437:
1432:
1427:
1422:
1417:
1412:
1407:
1402:
1400:هندسه سیالهای
1397:
1392:
1387:
1382:
1377:
1372:
1367:
1365:منیفلد مویشزون
1362:
1357:
1352:
1347:
1342:
1334:
1333:
1332:
1324:
1323:
1322:
1317:
1309:
1308:
1307:
1299:
1298:
1297:
1289:
1288:
1287:
1285:ئەندازەی جەبری
1279:
1278:
1277:
1272:
1264:
1263:
1262:
1254:
1253:
1252:
1239:
1234:to this file.
1228:
1227:
1222:
1217:
1212:
1207:
1202:
1197:
1192:
1187:
1182:
1177:
1172:
1170:Toric manifold
1167:
1162:
1157:
1152:
1147:
1142:
1137:
1132:
1127:
1122:
1117:
1115:Secant variety
1112:
1107:
1102:
1097:
1092:
1087:
1082:
1077:
1072:
1067:
1062:
1057:
1052:
1047:
1042:
1037:
1032:
1027:
1022:
1017:
1012:
1007:
1002:
997:
992:
987:
982:
977:
972:
967:
962:
957:
952:
947:
942:
937:
932:
927:
922:
917:
912:
907:
902:
897:
892:
887:
885:Fano fibration
882:
877:
872:
867:
862:
857:
852:
847:
842:
837:
832:
827:
822:
817:
812:
807:
802:
797:
792:
787:
782:
777:
772:
770:Barlow surface
767:
762:
757:
752:
747:
742:
737:
732:
725:is available.
718:
713:
712:
705:
701:
698:
692:
687:
682:
678:
677:
674:
671:
668:
665:
662:
654:
639:
634:
632:
631:
630:
628:
627:
623:
620:source of file
618:
616:
615:
614:
613:
611:
607:
606:source of file
595:
590:
588:
587:
586:
584:
578:
573:
571:
570:
569:
567:
566:
562:
557:
555:
554:
553:
552:
550:
546:
542:
530:
525:
523:
522:
521:
519:
518:
514:
509:
507:
506:
505:
504:
502:
498:
473:
472:
458:
457:
445:
444:
443:
442:
441:
437:
434:
432:
431:
430:
428:
427:
423:
418:
416:
415:
414:
413:
411:
407:
403:
399:
395:
391:
382:
377:
375:
372:
371:
370:
369:
357:
356:
353:
350:
341:
338:
337:
303:
275:
274:
273:
272:
262:
253:
252:
251:
245:
238:You are free:
225:
224:
206:
200:
199:
197:
194:
191:
182:
179:
175:
174:
171:
159:
158:
153:
149:
148:
143:
139:
138:
128:
119:
117:
114:
107:
106:
85:
75:
74:
40:
35:
34:
29:
24:
19:
9:
6:
4:
3:
2:
1591:
1582:
1580:
1571:
1568:
1567:
1565:
1561:
1558:
1557:
1555:
1551:
1548:
1546:
1543:
1541:
1538:
1536:
1533:
1532:
1530:
1526:
1523:
1522:
1520:
1516:
1513:
1512:
1510:
1506:
1503:
1502:
1500:
1496:
1493:
1491:
1488:
1486:
1483:
1481:
1478:
1477:
1475:
1471:
1468:
1466:
1463:
1461:
1458:
1456:
1453:
1451:
1448:
1446:
1443:
1441:
1438:
1436:
1435:رتبه خم بیضوی
1433:
1431:
1428:
1426:
1423:
1421:
1418:
1416:
1413:
1411:
1408:
1406:
1403:
1401:
1398:
1396:
1393:
1391:
1390:قضیه فالتینگز
1388:
1386:
1383:
1381:
1378:
1376:
1373:
1371:
1368:
1366:
1363:
1361:
1358:
1356:
1353:
1351:
1348:
1346:
1343:
1341:
1338:
1337:
1335:
1331:
1328:
1327:
1325:
1321:
1318:
1316:
1313:
1312:
1310:
1306:
1303:
1302:
1300:
1296:
1293:
1292:
1290:
1286:
1283:
1282:
1280:
1276:
1273:
1271:
1268:
1267:
1265:
1261:
1258:
1257:
1255:
1251:
1248:
1247:
1245:
1244:
1243:
1235:
1233:
1226:
1223:
1221:
1218:
1216:
1213:
1211:
1210:Wall-crossing
1208:
1206:
1203:
1201:
1198:
1196:
1193:
1191:
1188:
1186:
1183:
1181:
1178:
1176:
1175:Trident curve
1173:
1171:
1168:
1166:
1163:
1161:
1158:
1156:
1153:
1151:
1148:
1146:
1143:
1141:
1138:
1136:
1133:
1131:
1128:
1126:
1123:
1121:
1118:
1116:
1113:
1111:
1108:
1106:
1103:
1101:
1098:
1096:
1093:
1091:
1088:
1086:
1083:
1081:
1078:
1076:
1073:
1071:
1070:Normal degree
1068:
1066:
1063:
1061:
1058:
1056:
1053:
1051:
1048:
1046:
1043:
1041:
1038:
1036:
1033:
1031:
1028:
1026:
1023:
1021:
1020:Moduli scheme
1018:
1016:
1013:
1011:
1008:
1006:
1003:
1001:
998:
996:
993:
991:
988:
986:
983:
981:
978:
976:
973:
971:
968:
966:
963:
961:
960:Igusa quartic
958:
956:
953:
951:
948:
946:
943:
941:
938:
936:
933:
931:
928:
926:
923:
921:
918:
916:
913:
911:
908:
906:
903:
901:
898:
896:
893:
891:
888:
886:
883:
881:
878:
876:
873:
871:
868:
866:
863:
861:
858:
856:
853:
851:
848:
846:
843:
841:
838:
836:
833:
831:
828:
826:
823:
821:
818:
816:
813:
811:
808:
806:
803:
801:
798:
796:
793:
791:
788:
786:
783:
781:
778:
776:
773:
771:
768:
766:
763:
761:
758:
756:
753:
751:
748:
746:
743:
741:
738:
736:
733:
731:
728:
727:
726:
724:
710:
704:
699:
693:
691:
688:
686:
683:
680:
679:
675:
672:
669:
666:
663:
661:
660:
658:
637:
633:
621:
617:
593:
589:
576:
572:
560:
556:
528:
524:
512:
508:
483:
476:
468:
461:
448:
433:
421:
417:
380:
376:
373:
354:
347:
320:
319:
314:
310:
309:
304:
297:
296:
281:CC BY-SA 3.0
270:
266:
263:
260:
257:
256:
254:
249:
246:
243:
240:
239:
237:
236:
232:
229:
212:
190:
188:
172:
168:
163:
160:
157:
154:
150:
144:
140:
134:
129:
122:
103:
96:
95:
90:
86:
79:
78:
72:
63:
62:Original file
54:
50:
44:
39:
33:
30:
28:
25:
23:
20:
18:
15:
1576:
1420:ارزیاب (جبر)
1241:
1229:
1155:Tetrahedroid
1145:Tango bundle
1000:Line complex
890:Fermat cubic
875:Dwork family
805:Bracket ring
720:
656:
653:File history
316:
306:
264:
258:
247:
241:
184:
132:
102:You can help
92:
60:
22:File history
1460:بعد کودایرا
1425:میدان مانده
1395:هندسه حسابی
1385:ریخت متناهی
1350:پایه گروبنر
1250:هندسة جبرية
527:copyrighted
501:copyrighted
265:share alike
259:attribution
181:Source Code
124:Description
1340:هندسه جبری
1232:more links
1135:Steinerian
850:Cubic form
717:File usage
694:800 × 800
670:Dimensions
435:some value
162:Permission
27:File usage
1430:استک جبری
723:full list
667:Thumbnail
664:Date/Time
196:Licensing
173:cc-by-3.0
133:English:
68:image/png
1540:Wiskunde
1480:Geometri
1410:طیف حلقه
1355:خم بیضوی
1085:Osculant
835:Cayleyan
702:Rocchini
696:(163 KB)
467:Rocchini
402:Rocchini
355:Captions
248:to remix
242:to share
233:license.
146:Own work
681:current
676:Comment
420:creator
390:creator
379:depicts
359:English
187:POV-Ray
116:Summary
64:
745:Acnode
730:3-fold
152:Author
142:Source
1577:View
1445:لم چو
1230:View
673:User
335:true
332:true
326:GFDL
290:true
287:true
17:File
1515:幾何学
475:URL
406:URL
478::
463::
450::
51:|
45:.
321:.
169:)
165:(
104:.
70:)
55:.