Knowledge (XXG)

Fröberg conjecture

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610: 499: 347: 165: 224: 651: 352: 680: 644: 229: 685: 637: 55: 512: 670: 170: 566: 675: 564:
Iarrobino, Anthony (1997), "Inverse system of a symbolic power. III. Thin algebras and fat points",
617: 17: 585: 534: 621: 575: 524: 29: 597: 546: 593: 542: 550: 494:{\displaystyle {(1+t+t^{2}+\ldots )^{n}}{(1-t^{a_{1}})(1-t^{a_{2}})\cdots (1-t^{a_{k}})}} 32:
of a set of forms. It is named after Ralf Fröberg, who introduced it in Fröberg (
664: 609: 529: 580: 25: 589: 538: 342:{\displaystyle \mathbb {C} /\langle g_{1},g_{2},\ldots ,g_{k}\rangle } 40:
is a generalization introduced by Anthony Iarrobino (
160:{\displaystyle g_{1},g_{2},\ldots ,g_{k}\in \mathbb {C} } 625: 513:"An inequality for Hilbert series of graded algebras" 355: 232: 173: 58: 493: 341: 218: 159: 645: 8: 336: 291: 652: 638: 579: 528: 479: 474: 447: 442: 418: 413: 399: 392: 376: 356: 354: 330: 311: 298: 286: 277: 258: 245: 234: 233: 231: 219:{\displaystyle a_{1},a_{2},\ldots ,a_{k}} 210: 191: 178: 172: 148: 129: 116: 105: 104: 95: 76: 63: 57: 41: 33: 501:truncated at its first negative term. 52:Given generic homogeneous polynomials 7: 606: 604: 624:. You can help Knowledge (XXG) by 14: 226:resp. Then the Hilbert Series of 608: 487: 461: 455: 429: 426: 400: 389: 357: 283: 238: 154: 109: 1: 681:Unsolved problems in geometry 38:Fröberg–Iarrobino conjecture 702: 603: 530:10.7146/math.scand.a-12092 686:Algebraic geometry stubs 517:Mathematica Scandinavica 581:10.1023/A:1000155612073 48:Statement of Conjecture 36:, page 120). The 620:–related article is a 567:Compositio Mathematica 511:Fröberg, Ralf (1985), 495: 343: 220: 161: 496: 344: 221: 162: 353: 230: 171: 56: 28:about the possible 671:Algebraic geometry 618:algebraic geometry 491: 339: 216: 157: 22:Fröberg conjecture 18:algebraic geometry 633: 632: 30:Hilbert functions 693: 654: 647: 640: 612: 605: 600: 583: 560: 559: 558: 549:, archived from 532: 500: 498: 497: 492: 490: 486: 485: 484: 483: 454: 453: 452: 451: 425: 424: 423: 422: 398: 397: 396: 381: 380: 348: 346: 345: 340: 335: 334: 316: 315: 303: 302: 290: 282: 281: 263: 262: 250: 249: 237: 225: 223: 222: 217: 215: 214: 196: 195: 183: 182: 166: 164: 163: 158: 153: 152: 134: 133: 121: 120: 108: 100: 99: 81: 80: 68: 67: 701: 700: 696: 695: 694: 692: 691: 690: 661: 660: 659: 658: 563: 556: 554: 510: 507: 475: 470: 443: 438: 414: 409: 388: 372: 351: 350: 326: 307: 294: 273: 254: 241: 228: 227: 206: 187: 174: 169: 168: 144: 125: 112: 91: 72: 59: 54: 53: 50: 12: 11: 5: 699: 697: 689: 688: 683: 678: 673: 663: 662: 657: 656: 649: 642: 634: 631: 630: 613: 602: 601: 574:(3): 319–356, 561: 523:(2): 117–144, 506: 503: 489: 482: 478: 473: 469: 466: 463: 460: 457: 450: 446: 441: 437: 434: 431: 428: 421: 417: 412: 408: 405: 402: 395: 391: 387: 384: 379: 375: 371: 368: 365: 362: 359: 338: 333: 329: 325: 322: 319: 314: 310: 306: 301: 297: 293: 289: 285: 280: 276: 272: 269: 266: 261: 257: 253: 248: 244: 240: 236: 213: 209: 205: 202: 199: 194: 190: 186: 181: 177: 156: 151: 147: 143: 140: 137: 132: 128: 124: 119: 115: 111: 107: 103: 98: 94: 90: 87: 84: 79: 75: 71: 66: 62: 49: 46: 13: 10: 9: 6: 4: 3: 2: 698: 687: 684: 682: 679: 677: 674: 672: 669: 668: 666: 655: 650: 648: 643: 641: 636: 635: 629: 627: 623: 619: 614: 611: 607: 599: 595: 591: 587: 582: 577: 573: 569: 568: 562: 553:on 2013-02-13 552: 548: 544: 540: 536: 531: 526: 522: 518: 514: 509: 508: 504: 502: 480: 476: 471: 467: 464: 458: 448: 444: 439: 435: 432: 419: 415: 410: 406: 403: 393: 385: 382: 377: 373: 369: 366: 363: 360: 331: 327: 323: 320: 317: 312: 308: 304: 299: 295: 287: 278: 274: 270: 267: 264: 259: 255: 251: 246: 242: 211: 207: 203: 200: 197: 192: 188: 184: 179: 175: 149: 145: 141: 138: 135: 130: 126: 122: 117: 113: 101: 96: 92: 88: 85: 82: 77: 73: 69: 64: 60: 47: 45: 43: 39: 35: 31: 27: 23: 19: 626:expanding it 615: 571: 565: 555:, retrieved 551:the original 520: 516: 51: 37: 21: 15: 676:Conjectures 167:of degrees 665:Categories 557:2012-02-12 505:References 26:conjecture 590:0010-437X 539:0025-5521 468:− 459:⋯ 436:− 407:− 386:… 337:⟩ 321:… 292:⟨ 268:… 201:… 139:… 102:∈ 86:… 598:1473851 547:0813632 596:  588:  545:  537:  20:, the 616:This 24:is a 622:stub 586:ISSN 535:ISSN 42:1997 34:1985 576:doi 572:108 525:doi 349:is 44:). 16:In 667:: 594:MR 592:, 584:, 570:, 543:MR 541:, 533:, 521:56 519:, 515:, 653:e 646:t 639:v 628:. 578:: 527:: 488:) 481:k 477:a 472:t 465:1 462:( 456:) 449:2 445:a 440:t 433:1 430:( 427:) 420:1 416:a 411:t 404:1 401:( 394:n 390:) 383:+ 378:2 374:t 370:+ 367:t 364:+ 361:1 358:( 332:k 328:g 324:, 318:, 313:2 309:g 305:, 300:1 296:g 288:/ 284:] 279:n 275:x 271:, 265:, 260:2 256:x 252:, 247:1 243:x 239:[ 235:C 212:k 208:a 204:, 198:, 193:2 189:a 185:, 180:1 176:a 155:] 150:n 146:x 142:, 136:, 131:2 127:x 123:, 118:1 114:x 110:[ 106:C 97:k 93:g 89:, 83:, 78:2 74:g 70:, 65:1 61:g

Index

algebraic geometry
conjecture
Hilbert functions
1985
1997
"An inequality for Hilbert series of graded algebras"
doi
10.7146/math.scand.a-12092
ISSN
0025-5521
MR
0813632
the original
Compositio Mathematica
doi
10.1023/A:1000155612073
ISSN
0010-437X
MR
1473851
Stub icon
algebraic geometry
stub
expanding it
v
t
e
Categories
Algebraic geometry
Conjectures

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