The multiplier ideals of a sum of ideals
Author:
Mircea Mustata
Journal:
Trans. Amer. Math. Soc. 354 (2002), 205217
MSC (2000):
Primary 14B05; Secondary 14F17
Published electronically:
August 29, 2001
MathSciNet review:
1859032
Fulltext PDF Free Access
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Abstract: We prove that if , are nonzero sheaves of ideals on a complex smooth variety , then for every we have the following relation between the multiplier ideals of , and :
A similar formula holds for the asymptotic multiplier ideals of the sum of two graded systems of ideals. We use this result to approximate at a given point arbitrary multiplier ideals by multiplier ideals associated to zero dimensional ideals. This is applied to compare the multiplier ideals associated to a scheme in different embeddings.
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 [DS]
 Donatella Delfino and Irena Swanson, Integral closure of ideals in excellent local rings, J. Algebra 187 (1997), 422445. MR 98a:13014
 [DEL]
 JeanPierre Demailly, Lawrence Ein and Robert Lazarsfeld, A subadditivity property of multiplier ideals, Michigan Math. J. 48 (2000), 137156. CMP 2001:03
 [Ein]
 Lawrence Ein, Multiplier ideals, vanishing theorems and applications, in Algebraic geometry, Santa Cruz, 1995, 203220, volume 62 of Proc. Sympos. Pure Math., Amer. Math. Soc. 1997. MR 98m:14006
 [EL]
 Lawrence Ein and Robert Lazarsfeld, A geometric effective Nullstellensatz, Invent. Math. 137 (1999), no. 2, 427448. MR 2000j:14028
 [ELS]
 Lawrence Ein, Robert Lazarsfeld, and Karen Smith, Uniform bounds and symbolic powers on smooth varieties, Invent. Math. 144 (2001), 241252. CMP 2001:11
 [Ho]
 Jason Howald, Multiplier ideals of monomial ideals, Trans. Amer. Math. Soc. 353 (2001), 26652671. CMP 2001:11
 [Ka1]
 Yujiro Kawamata, Deformations of canonical singularities, J. Amer. Math. Soc. 12 (1999), no. 1, 8592. MR 99g:14003
 [Ka2]
 Yujiro Kawamata, On the extension problem of pluricanonical forms, in Algebraic Geometry: Hirzebruch 70 (Warsaw, 1998), Amer. Math. Soc., Providence, RI, 1999, pp. 193207. MR 2000i:14053
 [La]
 Robert Lazarsfeld, Multiplier ideals for algebraic geometers, lecture notes available at http://www.math.lsa.umich.edu/~rlaz, version of August 2000.
 [Mu]
 Mircea Mustata, Singularities of pairs via jet schemes, preprint 2001, arXiv: math. AG/0102201.
 [Siu]
 YumTong Siu, Invariance of plurigenera, Invent. Math. 134 (1998), no. 3, 661673. MR 99i:32035
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Additional Information
Mircea Mustata
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720 and Institute of Mathematics of The Romanian Academy, Bucharest, Romania
Email:
mustata@math.berkeley.edu
DOI:
http://dx.doi.org/10.1090/S0002994701028677
PII:
S 00029947(01)028677
Keywords:
Multiplier ideals,
log resolutions,
monomial ideals
Received by editor(s):
March 1, 2001
Published electronically:
August 29, 2001
Article copyright:
© Copyright 2001
American Mathematical Society
