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Category:Algebraic geometry

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Algebraic geometry is the place where the algebra involved in solving systems of simultaneous multivariable polynomial equations meets the geometry of curves, surfaces, and higher dimensional
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The following 200 pages are in this category, out of approximately 421 total.
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This category has the following 15 subcategories, out of 23 total.
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Decomposition theorem of Beilinson, Bernstein and Deligne
1574: 1180:Glossary of arithmetic and diophantine geometry 60: 1555:List of topologies on the category of schemes 762:Derived noncommutative algebraic geometry 414:Topological methods of algebraic geometry 1235:Grothendieck–Katz p-curvature conjecture 832:Distribution on a linear algebraic group 700:Cramer's theorem (algebraic curves) 473:This list may not reflect recent changes 1575: 807:Diagonal morphism (algebraic geometry) 468:Pages in category "Algebraic geometry" 1302:Hilbert series and Hilbert polynomial 1018:Fondements de la Géometrie Algébrique 36: 1550:Level structure (algebraic geometry) 1444:Italian school of algebraic geometry 162: 675:Correspondence (algebraic geometry) 13: 1545:Last geometric statement of Jacobi 1419:Inter-universal Teichmüller theory 1145:Geometric Langlands correspondence 486: 174: 161: 14: 1599: 1312:Hilbert's arithmetic of ends 1240:Grothendieck's Galois theory 1043:Foundations of Algebraic Geometry 747:Degeneration (algebraic geometry) 595:Combinatorial commutative algebra 1317:Hilbert's fifteenth problem 1277:Harder–Narasimhan stratification 827:Discrepancy (algebraic geometry) 1088:Functor represented by a scheme 1175:Glossary of algebraic geometry 1120:Generalized Riemann hypothesis 812:Differential of the first kind 670:Convexity (algebraic geometry) 605:Comodule over a Hopf algebroid 520:Castelnuovo–Mumford regularity 1: 1483:K-stability of Fano varieties 600:Combinatorial mirror symmetry 540:Chevalley restriction theorem 1394:Imaginary line (mathematics) 1352:Homotopy associative algebra 1140:Geometric class field theory 901:Esquisse d'un Programme 655:Constructible set (topology) 466: 7: 1023:Formal holomorphic function 10: 1604: 1583:Fields of abstract algebra 1155:Geometrically regular ring 757:Derived algebraic geometry 259:Localization (mathematics) 16:The main article for this 15: 1048:Fourier–Deligne transform 742:Deformation (mathematics) 635:Cone (algebraic geometry) 580:Coherent sheaf cohomology 1409:Infinitesimal cohomology 1287:Hasse–Weil zeta function 1185:Gopakumar–Vafa invariant 615:Complex analytic variety 447:Algebraic geometry stubs 1322:Hironaka's example 1307:Hilbert–Samuel function 1230:Grothendieck connection 1225:Gromov–Witten invariant 948:Faithfully flat descent 896:Erdős–Diophantine graph 842:Donaldson–Thomas theory 390:Structures on manifolds 332:Real algebraic geometry 299:Noncommutative geometry 1503:Kleiman's theorem 1461:Jouanolou's trick 1347:Homogeneous polynomial 1105:Gauss–Manin connection 978:Field with one element 885:Equidimensional scheme 777:Derived tensor product 715:Crystalline cohomology 1434:Irreducible component 1429:Inverse image functor 1337:Hodge–Arakelov theory 1160:Gibbons–Hawking space 953:Fake projective space 817:Dimension of a scheme 797:Determinantal variety 787:Descent along torsors 782:Descent (mathematics) 752:Deligne–Mumford stack 710:Crystal (mathematics) 695:Cramer's paradox 630:Condensed mathematics 610:Complete intersection 590:Cohomology of a stack 585:Cohomological descent 555:Chow group of a stack 505:Canonical singularity 1528:Kummer configuration 879:Enumerative geometry 792:Dessin d'enfant 665:Contraction morphism 525:Categorical quotient 1513:Kodaira–Spencer map 1508:Klein configuration 1488:Kähler differential 1473:K-groups of a field 1456:Jacobian conjecture 1424:Intersection number 1250:Group-scheme action 1190:Gordan's lemma 1068:Frobenius splitting 1038:Formally smooth map 973:Field of definition 931:Exceptional divisor 906:Étale homotopy type 852:Du Bois singularity 660:Constructible sheaf 570:Cohen–Macaulay ring 515:Cartier isomorphism 495:Calabi–Yau manifold 222:Intersection theory 185:Cohomology theories 43:Commutative algebra 31:algebraic varieties 1588:Fields of geometry 1523:Kuga fiber variety 1377:Hypertoric variety 1367:Hyperplane section 1292:Hessenberg variety 1282:Hartshorne ellipse 1150:Geometric quotient 1073:Fröberg conjecture 1063:Frobenius manifold 1053:Frankel conjecture 1013:Flip (mathematics) 874:Elimination theory 705:Crepant resolution 373:Singularity theory 37:Related categories 23:Algebraic geometry 1518:Koszul cohomology 1399:Implicit function 1342:Hodge–Tate module 1195:Gorenstein scheme 1083:Fujita conjecture 837:Divisorial scheme 680:Cotangent complex 620:Complex dimension 427:Tropical geometry 312:Nonlinear algebra 53:Geometric algebra 1595: 1498:Kobayashi metric 1439:Irrelevant ideal 1332:Hodge conjecture 1200:Grassmann bundle 1135:Generic property 1125:Generic flatness 1115:General position 1110:General elephant 958:Family of curves 887: 822:Direction cosine 625:Complex geometry 452: 432: 419: 412: 395: 388: 378: 371: 361: 354: 337: 317: 304: 284: 264: 244: 239:Invariant theory 237: 227: 207: 202:Complex geometry 200: 190: 48:Computer algebra 1603: 1602: 1598: 1597: 1596: 1594: 1593: 1592: 1573: 1572: 1571: 1561: 1560: 1559: 1532: 1493:Kähler manifold 1465: 1448: 1414:Injective sheaf 1381: 1357:Horrocks bundle 1264: 1260:Groupoid object 1210:Griffiths group 1100:Galois geometry 1092: 988:Finite morphism 935: 891:Equisingularity 883: 866: 857:Dualizing sheaf 847:Drinfeld module 729: 685:Cotangent sheaf 545:Chordal variety 510:Cartan subgroup 465: 459: 458: 457: 454: 453: 437: 434: 433: 421: 420: 409: 400: 397: 396: 385: 380: 379: 368: 363: 362: 351: 342: 339: 338: 322: 319: 318: 306: 305: 289: 286: 285: 269: 266: 265: 249: 246: 245: 234: 229: 228: 212: 209: 208: 197: 192: 191: 160: 159: 158: 157: 63: 39: 27: 12: 11: 5: 1601: 1591: 1590: 1585: 1558: 1557: 1552: 1547: 1542: 1536: 1533: 1531: 1530: 1525: 1520: 1515: 1510: 1505: 1500: 1495: 1490: 1485: 1480: 1475: 1469: 1466: 1464: 1463: 1458: 1452: 1449: 1447: 1446: 1441: 1436: 1431: 1426: 1421: 1416: 1411: 1406: 1401: 1396: 1391: 1385: 1382: 1380: 1379: 1374: 1369: 1364: 1362:Hurwitz scheme 1359: 1354: 1349: 1344: 1339: 1334: 1329: 1327:Hitchin system 1324: 1319: 1314: 1309: 1304: 1299: 1297:Hilbert scheme 1294: 1289: 1284: 1279: 1274: 1268: 1265: 1263: 1262: 1257: 1252: 1247: 1242: 1237: 1232: 1227: 1222: 1217: 1212: 1207: 1202: 1197: 1192: 1187: 1182: 1177: 1172: 1167: 1162: 1157: 1152: 1147: 1142: 1137: 1132: 1127: 1122: 1117: 1112: 1107: 1102: 1096: 1093: 1091: 1090: 1085: 1080: 1078:Fujiki class C 1075: 1070: 1065: 1060: 1055: 1050: 1045: 1040: 1035: 1030: 1025: 1020: 1015: 1010: 1005: 1000: 995: 990: 985: 983:Finite algebra 980: 975: 970: 965: 963:Fano fibration 960: 955: 950: 945: 939: 936: 934: 933: 928: 926:Excellent ring 923: 921:Euler sequence 918: 916:Étale topology 913: 911:Étale spectrum 908: 903: 898: 893: 888: 881: 876: 870: 867: 865: 864: 859: 854: 849: 844: 839: 834: 829: 824: 819: 814: 809: 804: 799: 794: 789: 784: 779: 774: 769: 767:Derived scheme 764: 759: 754: 749: 744: 739: 733: 730: 728: 727: 722: 717: 712: 707: 702: 697: 692: 687: 682: 677: 672: 667: 662: 657: 652: 647: 642: 640:Cone of curves 637: 632: 627: 622: 617: 612: 607: 602: 597: 592: 587: 582: 577: 575:Coherent sheaf 572: 567: 562: 557: 552: 547: 542: 537: 532: 527: 522: 517: 512: 507: 502: 500:Canonical ring 497: 491: 488: 487: 469: 464:) (next page) 456: 455: 445: 444: 441: 438: 436: 435: 425: 424: 422: 408: 407: 404: 401: 399: 398: 384: 383: 381: 367: 366: 364: 350: 349: 346: 343: 341: 340: 330: 329: 326: 323: 321: 320: 310: 309: 307: 297: 296: 293: 290: 288: 287: 277: 276: 273: 270: 268: 267: 257: 256: 253: 250: 248: 247: 233: 232: 230: 220: 219: 216: 213: 211: 210: 196: 195: 193: 183: 182: 179: 176: 175: 165: 156: 155: 75: 70: 64: 62: 59: 57: 56: 55: 50: 45: 38: 35: 9: 6: 4: 3: 2: 1600: 1589: 1586: 1584: 1581: 1580: 1578: 1569: 1565: 1564:previous page 1556: 1553: 1551: 1548: 1546: 1543: 1541: 1538: 1537: 1534: 1529: 1526: 1524: 1521: 1519: 1516: 1514: 1511: 1509: 1506: 1504: 1501: 1499: 1496: 1494: 1491: 1489: 1486: 1484: 1481: 1479: 1476: 1474: 1471: 1470: 1467: 1462: 1459: 1457: 1454: 1453: 1450: 1445: 1442: 1440: 1437: 1435: 1432: 1430: 1427: 1425: 1422: 1420: 1417: 1415: 1412: 1410: 1407: 1405: 1402: 1400: 1397: 1395: 1392: 1390: 1389:Igusa variety 1387: 1386: 1383: 1378: 1375: 1373: 1370: 1368: 1365: 1363: 1360: 1358: 1355: 1353: 1350: 1348: 1345: 1343: 1340: 1338: 1335: 1333: 1330: 1328: 1325: 1323: 1320: 1318: 1315: 1313: 1310: 1308: 1305: 1303: 1300: 1298: 1295: 1293: 1290: 1288: 1285: 1283: 1280: 1278: 1275: 1273: 1270: 1269: 1266: 1261: 1258: 1256: 1253: 1251: 1248: 1246: 1245:Group functor 1243: 1241: 1238: 1236: 1233: 1231: 1228: 1226: 1223: 1221: 1218: 1216: 1215:Gröbner basis 1213: 1211: 1208: 1206: 1203: 1201: 1198: 1196: 1193: 1191: 1188: 1186: 1183: 1181: 1178: 1176: 1173: 1171: 1168: 1166: 1163: 1161: 1158: 1156: 1153: 1151: 1148: 1146: 1143: 1141: 1138: 1136: 1133: 1131: 1130:Generic point 1128: 1126: 1123: 1121: 1118: 1116: 1113: 1111: 1108: 1106: 1103: 1101: 1098: 1097: 1094: 1089: 1086: 1084: 1081: 1079: 1076: 1074: 1071: 1069: 1066: 1064: 1061: 1059: 1056: 1054: 1051: 1049: 1046: 1044: 1041: 1039: 1036: 1034: 1033:Formal scheme 1031: 1029: 1028:Formal moduli 1026: 1024: 1021: 1019: 1016: 1014: 1011: 1009: 1008:Flat topology 1006: 1004: 1001: 999: 998:Flat function 996: 994: 991: 989: 986: 984: 981: 979: 976: 974: 971: 969: 966: 964: 961: 959: 956: 954: 951: 949: 946: 944: 941: 940: 937: 932: 929: 927: 924: 922: 919: 917: 914: 912: 909: 907: 904: 902: 899: 897: 894: 892: 889: 886: 882: 880: 877: 875: 872: 871: 868: 863: 860: 858: 855: 853: 850: 848: 845: 843: 840: 838: 835: 833: 830: 828: 825: 823: 820: 818: 815: 813: 810: 808: 805: 803: 800: 798: 795: 793: 790: 788: 785: 783: 780: 778: 775: 773: 772:Derived stack 770: 768: 765: 763: 760: 758: 755: 753: 750: 748: 745: 743: 740: 738: 735: 734: 731: 726: 723: 721: 718: 716: 713: 711: 708: 706: 703: 701: 698: 696: 693: 691: 688: 686: 683: 681: 678: 676: 673: 671: 668: 666: 663: 661: 658: 656: 653: 651: 648: 646: 643: 641: 638: 636: 633: 631: 628: 626: 623: 621: 618: 616: 613: 611: 608: 606: 603: 601: 598: 596: 593: 591: 588: 586: 583: 581: 578: 576: 573: 571: 568: 566: 563: 561: 558: 556: 553: 551: 548: 546: 543: 541: 538: 536: 533: 531: 530:Catenary ring 528: 526: 523: 521: 518: 516: 513: 511: 508: 506: 503: 501: 498: 496: 493: 492: 489: 484: 480: 479:previous page 476: 474: 467: 463: 462:previous page 448: 443: 442: 439: 428: 423: 415: 411: 406: 405: 402: 391: 387: 382: 374: 370: 365: 357: 356:Scheme theory 353: 348: 347: 344: 333: 328: 327: 324: 313: 308: 300: 295: 294: 291: 280: 279:Moduli theory 275: 274: 271: 260: 255: 254: 251: 240: 236: 231: 223: 218: 217: 214: 203: 199: 194: 186: 181: 180: 177: 173:) (next page) 172: 171:previous page 168: 164:Subcategories 163: 154: 151: 148: 145: 142: 139: 136: 133: 130: 127: 124: 121: 118: 115: 112: 109: 106: 103: 100: 97: 94: 91: 88: 85: 82: 79: 76: 74: 71: 69: 66: 65: 54: 51: 49: 46: 44: 41: 40: 34: 32: 25: 24: 19: 1540:ℓ-adic sheaf 1372:Hypersurface 1205:Grassmannian 1165:GIT quotient 968:Fano variety 862:Dwork family 725:Cyclic cover 645:Conic bundle 560:Chow variety 470: 166: 28: 21: 1478:K-stability 1255:Group-stack 1220:Gröbner fan 1170:GKM variety 1003:Flat module 993:Flag bundle 565:Codimension 418:(1 C, 32 P) 394:(2 C, 54 P) 377:(3 C, 53 P) 360:(1 C, 40 P) 243:(1 C, 60 P) 1577:Categories 1404:Ind-scheme 1272:H topology 1058:Frobenioid 720:Cubic form 550:Chow group 206:(2 C, 3 P) 1568:next page 943:F-crystal 802:Dévissage 483:next page 61:Contents 690:Cox ring 650:Conifold 535:Cayleyan 18:category 451:(182 P) 336:(43 P) 303:(18 P) 283:(26 P) 226:(13 P) 189:(50 P) 431:(6 P) 316:(3 P) 263:(9 P) 1566:) ( 481:) ( 73:0–9 68:Top 20:is 1579:: 1570:) 475:. 449:‎ 429:‎ 416:‎ 392:‎ 375:‎ 358:‎ 334:‎ 314:‎ 301:‎ 281:‎ 261:‎ 241:‎ 224:‎ 204:‎ 187:‎ 33:. 1562:( 1535:L 1468:K 1451:J 1384:I 1267:H 1095:G 938:F 869:E 732:D 490:C 485:) 477:( 460:( 440:Σ 403:T 345:S 325:R 292:N 272:M 252:L 215:I 178:C 169:( 153:Z 150:Y 147:X 144:W 141:V 138:U 135:T 132:S 129:R 126:Q 123:P 120:O 117:N 114:M 111:L 108:K 105:J 102:I 99:H 96:G 93:F 90:E 87:D 84:C 81:B 78:A 26:.

Index

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Algebraic geometry
algebraic varieties
Commutative algebra
Computer algebra
Geometric algebra
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