The multiplier ideals of a sum of ideals

Author:
Mircea Mustata

Journal:
Trans. Amer. Math. Soc. **354** (2002), 205-217

MSC (2000):
Primary 14B05; Secondary 14F17

DOI:
https://doi.org/10.1090/S0002-9947-01-02867-7

Published electronically:
August 29, 2001

MathSciNet review:
1859032

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Abstract | References | Similar Articles | Additional Information

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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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:
https://doi.org/10.1090/S0002-9947-01-02867-7

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