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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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When does the subadditivity theorem for multiplier ideals hold?
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by Shunsuke Takagi and Kei-ichi Watanabe PDF
Trans. Amer. Math. Soc. 356 (2004), 3951-3961 Request permission

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
  • MR Author ID: 216208
  • Email: watanabe@math.chs.nihon-u.ac.jp
  • 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.
  • © Copyright 2004 American Mathematical Society
  • 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
  • MathSciNet review: 2058513