When does the subadditivity theorem for multiplier ideals hold?

Takagi, Shunsuke; Watanabe, Kei-ichi

doi:10.1090/S0002-9947-04-03436-1

When does the subadditivity theorem for multiplier ideals hold?
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by Shunsuke Takagi and Kei-ichi Watanabe

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

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

Published electronically: February 4, 2004

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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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