915:
413:
537:
139:
630:
568:
298:
456:
956:
261:
212:
788:
227:
949:
985:
942:
699:
786:
Nadel, Alan
Michael (1989), "Multiplier ideal sheaves and existence of Kähler-Einstein metrics of positive scalar curvature",
64:
318:
975:
215:
980:
145:
673:
461:
577:
223:
651:
677:
641:
542:
914:
157:
are a finite set of local generators of the ideal. Multiplier ideals were independently introduced by
871:
797:
739:
17:
682:
301:
922:
40:
36:
28:
266:
244:
195:
895:
861:
815:
729:
713:
665:
841:
695:
421:
47:
926:
879:
831:
805:
687:
891:
827:
779:
709:
887:
823:
775:
705:
875:
801:
743:
760:
44:
836:
761:"Adjoints and polars of simple complete ideals in two-dimensional regular local rings"
969:
899:
222:. Multiplier ideals are often applied in tandem with vanishing theorems such as the
852:
Siu, Yum-Tong (2005), "Multiplier ideal sheaves in complex and algebraic geometry",
717:
691:
789:
Proceedings of the
National Academy of Sciences of the United States of America
646:
810:
845:
161:(who worked with sheaves over complex manifolds rather than ideals) and
883:
866:
819:
734:
724:
Lazarsfeld, Robert (2009), "A short course on multiplier ideals",
599:
549:
349:
218:
measures singularities coming from the fractional parts of
768:
Bulletin de la Société Mathématique de
Belgique. SĂ©rie A
930:
308:(e.g., Hironaka's resolution). The multiplier ideal of
168:
Multiplier ideals are discussed in the survey articles
134:{\displaystyle {\frac {|h|^{2}}{\sum |f_{i}^{2}|^{c}}}}
408:{\displaystyle J(D)=\mu _{*}{\mathcal {O}}(K_{X'/X}-)}
580:
545:
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321:
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247:
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67:
624:
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531:
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292:
255:
206:
133:
169:
666:"An informal introduction to multiplier ideals"
950:
672:, Math. Sci. Res. Inst. Publ., vol. 51,
532:{\displaystyle K_{X'/X}=K_{X'}-\mu ^{*}K_{X}}
8:
664:Blickle, Manuel; Lazarsfeld, Robert (2004),
625:{\displaystyle J(D)={\mathcal {O}}_{X}(-D)}
957:
943:
177:
865:
835:
809:
733:
681:
604:
598:
597:
579:
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268:
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122:
117:
110:
105:
96:
85:
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71:
68:
66:
162:
158:
18:Multiplier ideal (algebraic geometry)
7:
911:
909:
54:consists (locally) of the functions
752:Positivity in algebraic geometry II
458:is the relative canonical divisor:
173:
929:. You can help Knowledge (XXG) by
563:{\displaystyle {\mathcal {O}}_{X}}
228:Kawamata–Viehweg vanishing theorem
165:, who called them adjoint ideals.
25:
913:
237:be a smooth complex variety and
170:Blickle & Lazarsfeld (2004)
619:
610:
590:
584:
402:
399:
383:
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331:
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284:
118:
97:
81:
72:
1:
670:Trends in commutative algebra
692:10.1017/CBO9780511756382.004
293:{\displaystyle \mu :X'\to X}
256:{\displaystyle \mathbb {Q} }
207:{\displaystyle \mathbb {Q} }
750:Lazarsfeld, Robert (2004).
188:In algebraic geometry, the
1002:
908:
754:. Berlin: Springer-Verlag.
674:Cambridge University Press
539:. It is an ideal sheaf of
986:Commutative algebra stubs
854:Science China Mathematics
224:Kodaira vanishing theorem
451:{\displaystyle K_{X'/X}}
811:10.1073/pnas.86.19.7299
759:Lipman, Joseph (1993),
652:Nadel vanishing theorem
925:-related article is a
626:
564:
533:
452:
409:
294:
257:
208:
135:
642:Canonical singularity
627:
565:
534:
453:
410:
295:
258:
209:
136:
578:
543:
462:
422:
319:
267:
263:-divisor on it. Let
245:
196:
65:
976:Commutative algebra
923:commutative algebra
876:2005ScChA..48....1S
802:1989PNAS...86.7299N
744:2009arXiv0901.0651L
676:, pp. 87–114,
115:
29:commutative algebra
981:Algebraic geometry
884:10.1007/BF02884693
726:2008 PCMI Lectures
622:
574:is integral, then
560:
529:
448:
405:
290:
253:
204:
184:Algebraic geometry
146:locally integrable
131:
101:
50:and a real number
938:
937:
796:(19): 7299–7300,
178:Lazarsfeld (2009)
129:
16:(Redirected from
993:
959:
952:
945:
917:
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902:
869:
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839:
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765:
755:
746:
737:
720:
685:
631:
629:
628:
623:
609:
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602:
569:
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566:
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291:
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262:
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252:
213:
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203:
192:of an effective
190:multiplier ideal
140:
138:
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128:
127:
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100:
91:
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89:
84:
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35:associated to a
33:multiplier ideal
21:
1001:
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994:
992:
991:
990:
966:
965:
964:
963:
906:
851:
785:
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758:
749:
723:
702:
683:10.1.1.241.4916
663:
660:
638:
596:
576:
575:
546:
541:
540:
519:
509:
496:
491:
470:
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460:
459:
430:
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419:
386:
362:
357:
337:
317:
316:
276:
265:
264:
243:
242:
194:
193:
186:
156:
116:
92:
79:
70:
63:
62:
23:
22:
15:
12:
11:
5:
999:
997:
989:
988:
983:
978:
968:
967:
962:
961:
954:
947:
939:
936:
935:
918:
904:
903:
849:
783:
774:(1): 223–244,
756:
747:
721:
700:
659:
656:
655:
654:
649:
644:
637:
634:
621:
618:
615:
612:
607:
601:
595:
592:
589:
586:
583:
557:
551:
526:
522:
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512:
508:
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499:
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468:
445:
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377:
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324:
302:log resolution
289:
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275:
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251:
202:
185:
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152:
142:
141:
125:
120:
113:
108:
104:
99:
95:
88:
83:
78:
74:
24:
14:
13:
10:
9:
6:
4:
3:
2:
998:
987:
984:
982:
979:
977:
974:
973:
971:
960:
955:
953:
948:
946:
941:
940:
934:
932:
928:
924:
919:
916:
912:
907:
901:
897:
893:
889:
885:
881:
877:
873:
868:
863:
859:
855:
850:
847:
843:
838:
833:
829:
825:
821:
817:
812:
807:
803:
799:
795:
791:
790:
784:
781:
777:
773:
769:
762:
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753:
748:
745:
741:
736:
731:
727:
722:
719:
715:
711:
707:
703:
701:9780521831956
697:
693:
689:
684:
679:
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671:
667:
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661:
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616:
613:
605:
593:
587:
581:
573:
555:
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520:
514:
510:
506:
500:
497:
492:
488:
483:
479:
474:
471:
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443:
439:
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431:
426:
396:
391:
387:
380:
375:
371:
366:
363:
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342:
338:
334:
328:
322:
315:
314:
313:
311:
307:
303:
287:
280:
277:
273:
270:
241:an effective
240:
236:
231:
229:
225:
221:
217:
191:
183:
181:
179:
175:
171:
166:
164:
163:Lipman (1993)
160:
155:
151:
147:
123:
111:
106:
102:
93:
86:
76:
61:
60:
59:
57:
53:
49:
46:
42:
38:
34:
30:
19:
931:expanding it
920:
905:
867:math/0504259
860:(S1): 1–31,
857:
853:
793:
787:
771:
767:
751:
725:
669:
571:
417:
309:
305:
238:
234:
232:
219:
189:
187:
167:
159:Nadel (1989)
153:
149:
148:, where the
143:
55:
51:
32:
26:
970:Categories
658:References
647:Test ideal
174:Siu (2005)
58:such that
900:119163294
735:0901.0651
678:CiteSeerX
614:−
515:∗
511:μ
507:−
392:∗
388:μ
381:−
343:∗
339:μ
285:→
271:μ
94:∑
846:16594070
718:10215098
636:See also
501:′
475:′
435:′
367:′
281:′
226:and the
892:2156488
872:Bibcode
828:1015491
798:Bibcode
780:1316244
740:Bibcode
710:2132649
216:divisor
48:variety
45:complex
43:over a
898:
890:
844:
837:298048
834:
826:
818:
778:
716:
708:
698:
680:
418:where
176:, and
41:ideals
31:, the
921:This
896:S2CID
862:arXiv
820:34630
816:JSTOR
764:(PDF)
730:arXiv
714:S2CID
570:. If
300:be a
37:sheaf
927:stub
842:PMID
696:ISBN
233:Let
880:doi
832:PMC
806:doi
688:doi
312:is
304:of
144:is
39:of
27:In
972::
894:,
888:MR
886:,
878:,
870:,
858:48
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794:86
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772:45
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704:,
694:,
686:,
668:,
632:.
230:.
180:.
172:,
958:e
951:t
944:v
933:.
882::
874::
864::
808::
800::
742::
732::
690::
620:)
617:D
611:(
606:X
600:O
594:=
591:)
588:D
585:(
582:J
572:D
556:X
550:O
525:X
521:K
498:X
493:K
489:=
484:X
480:/
472:X
467:K
444:X
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432:X
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376:X
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335:=
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