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Fujita conjecture

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190: 413: 263: 177:. For three-dimensional algebraic varieties, Ein and Lazarsfeld in 1993 proved the first part of the Fujita conjecture, i.e. that 154: 398: 336: 403: 44: 211:(1993), "Global generation of pluricanonical and adjoint linear series on smooth projective threefolds.", 408: 174: 92: 377: 25: 259: 208: 126: 310:
Siu, Yum-Tong (1996), "The Fujita conjecture and the extension theorem of Ohsawa-Takegoshi",
359: 351: 323: 290: 251: 220: 162: 81: 29: 373: 319: 302: 273: 244:
Fujita, Takao (1987), "On polarized manifolds whose adjoint bundles are not semipositive",
234: 369: 327: 315: 298: 269: 230: 225: 392: 51: 41: 381: 157:(and its complex analytic variant). Fujita conjecture provides an explicit bound on 337:"A tight closure proof of Fujita's freeness conjecture for very ample line bundles" 250:, Adv. Stud. Pure Math., vol. 10, North-Holland, Amsterdam, pp. 167–178, 245: 294: 17: 106: 255: 355: 364: 32:. It is named after Takao Fujita, who formulated it in 1985. 314:, World Sci. Publ., River Edge, NJ, pp. 577–592, 40:
In complex geometry, the conjecture states that for a
281:Helmke, Stefan (1997), "On Fujita's conjecture", 173:For surfaces the Fujita conjecture follows from 8: 363: 312:Geometric complex analysis (Hayama, 1995) 224: 7: 14: 226:10.1090/S0894-0347-1993-1207013-5 247:Algebraic geometry, Sendai, 1985 24:is a problem in the theories of 181:≥4 implies global generation. 153:is very ample by the standard 1: 414:Unsolved problems in geometry 295:10.1215/S0012-7094-97-08807-4 430: 283:Duke Mathematical Journal 155:Serre's vanishing theorem 335:Smith, Karen E. (2000), 161:, which is optimal for 45:holomorphic line bundle 356:10.1007/s002080000094 344:Mathematische Annalen 256:10.2969/aspm/01010167 82:canonical line bundle 136:Note that for large 213:J. Amer. Math. Soc. 93:spanned by sections 22:Fujita's conjecture 399:Algebraic geometry 209:Lazarsfeld, Robert 58:, the line bundle 26:algebraic geometry 404:Complex manifolds 265:978-4-86497-068-6 195:extension theorem 191:Ohsawa–Takegoshi 163:projective spaces 127:complex dimension 54:complex manifold 30:complex manifolds 421: 384: 367: 341: 330: 305: 276: 237: 228: 175:Reider's theorem 140:the line bundle 429: 428: 424: 423: 422: 420: 419: 418: 389: 388: 339: 334: 309: 280: 266: 243: 207:Ein, Lawrence; 206: 203: 187: 171: 148: 79: 66: 38: 12: 11: 5: 427: 425: 417: 416: 411: 406: 401: 391: 390: 387: 386: 350:(2): 285–293, 332: 307: 289:(2): 201–216, 278: 264: 240: 239: 219:(4): 875–903, 202: 199: 198: 197: 186: 183: 170: 167: 144: 119: 118: 104: 75: 62: 37: 34: 13: 10: 9: 6: 4: 3: 2: 426: 415: 412: 410: 407: 405: 402: 400: 397: 396: 394: 383: 379: 375: 371: 366: 365:2027.42/41935 361: 357: 353: 349: 345: 338: 333: 329: 325: 321: 317: 313: 308: 304: 300: 296: 292: 288: 284: 279: 275: 271: 267: 261: 257: 253: 249: 248: 242: 241: 236: 232: 227: 222: 218: 214: 210: 205: 204: 200: 196: 194: 189: 188: 184: 182: 180: 176: 168: 166: 164: 160: 156: 152: 147: 143: 139: 134: 132: 128: 124: 116: 112: 108: 105: 102: 98: 94: 91: 90: 89: 87: 83: 78: 74: 70: 65: 61: 57: 53: 49: 46: 43: 35: 33: 31: 27: 23: 19: 347: 343: 311: 286: 282: 246: 216: 212: 192: 178: 172: 158: 150: 145: 141: 137: 135: 130: 122: 120: 114: 110: 100: 96: 85: 76: 72: 68: 63: 59: 55: 47: 39: 21: 15: 409:Conjectures 169:Known cases 18:mathematics 393:Categories 328:0941.32021 201:References 107:very ample 103:+ 1 ; 36:Statement 382:55051810 185:See also 42:positive 374:1764238 320:1453639 303:1455517 274:0946238 235:1207013 125:is the 71:(where 52:compact 380:  372:  326:  318:  301:  272:  262:  233:  121:where 95:when 88:) is 378:S2CID 340:(PDF) 109:when 80:is a 50:on a 260:ISBN 117:+ 2, 28:and 360:hdl 352:doi 348:317 324:Zbl 291:doi 252:doi 221:doi 129:of 84:of 16:In 395:: 376:, 370:MR 368:, 358:, 346:, 342:, 322:, 316:MR 299:MR 297:, 287:88 285:, 270:MR 268:, 258:, 231:MR 229:, 215:, 165:. 149:⊗ 133:. 113:≥ 99:≥ 67:⊗ 20:, 385:. 362:: 354:: 331:. 306:. 293:: 277:. 254:: 238:. 223:: 217:6 193:L 179:m 159:m 151:L 146:M 142:K 138:m 131:M 123:n 115:n 111:m 101:n 97:m 86:M 77:M 73:K 69:L 64:M 60:K 56:M 48:L

Index

mathematics
algebraic geometry
complex manifolds
positive
holomorphic line bundle
compact
canonical line bundle
spanned by sections
very ample
complex dimension
Serre's vanishing theorem
projective spaces
Reider's theorem
Ohsawa–Takegoshi L extension theorem
Lazarsfeld, Robert
doi
10.1090/S0894-0347-1993-1207013-5
MR
1207013
Algebraic geometry, Sendai, 1985
doi
10.2969/aspm/01010167
ISBN
978-4-86497-068-6
MR
0946238
doi
10.1215/S0012-7094-97-08807-4
MR
1455517

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