When does the subadditivity theorem for multiplier ideals hold?

Authors:
Shunsuke Takagi and Kei-ichi Watanabe

Translated by:

Journal:
Trans. Amer. Math. Soc. **356** (2004), 3951-3961

MSC (2000):
Primary 13B22; Secondary 14J17

DOI:
https://doi.org/10.1090/S0002-9947-04-03436-1

Published electronically:
February 4, 2004

MathSciNet review:
2058513

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Abstract | References | Similar Articles | Additional Information

Abstract: Demailly, Ein and Lazarsfeld proved the subadditivity theorem for multiplier ideals on nonsingular varieties, which states the multiplier ideal of the product of ideals is contained in the product of the individual multiplier ideals. We prove that, in the two-dimensional case, the subadditivity theorem holds on log terminal singularities. However, in the higher dimensional case, we have several counterexamples. We consider the subadditivity theorem for monomial ideals on toric rings and construct a counterexample on a three-dimensional toric ring.

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Additional Information

**Shunsuke Takagi**

Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1, Komaba, Meguro, Tokyo 153-8914, Japan

Email:
stakagi@ms.u-tokyo.ac.jp

**Kei-ichi Watanabe**

Affiliation:
Department of Mathematics, College of Humanities and Sciences, Nihon University, Setagaya-ku, Tokyo 156–0045, Japan

Email:
watanabe@math.chs.nihon-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9947-04-03436-1

Received by editor(s):
January 2, 2003

Received by editor(s) in revised form:
June 3, 2003

Published electronically:
February 4, 2004

Additional Notes:
The authors thank MSRI for the support and hospitality during their stay in the fall of 2002. The second author was partially supported by Grants-in-Aid in Scientific Researches, 13440015, 13874006; and his stay at MSRI was supported by the Bunri Fund, Nihon University.

Article copyright:
© Copyright 2004
American Mathematical Society