When does the subadditivity theorem for multiplier ideals hold?

Details When does the subadditivity theorem for multiplier ideals hold? When does the subadditivity theorem for multiplier ideals hold?

2002-12-25

arxiv.org/abs/math/0212340v2

Mathematics

Commutative Algebra

12 pages, AMS-LaTeX; v.2: minor changes, to appear in Trans. Amer. Math. Soc

Scientific paper

Demailly, Ein and Lazarsfeld \cite{DEL} proved the subadditivity theorem for multiplier ideals, which states the multiplier ideal of the product of ideals is contained in the product of the individual multiplier ideals, on non-singular varieties. We prove that, in two-dimensional case, the subadditivity theorem holds on log-terminal singularities. However, in higher dimensional case, we have several counter-examples. We consider the subadditivity theorem for monomial ideals on toric rings, and construct a counter-example on a three-dimensional toric ring.

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