When does the subadditivity theorem for multiplier ideals hold?
Commutative Algebra
2007-05-23 v2 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.math/0212340,
title = {When does the subadditivity theorem for multiplier ideals hold?},
author = {Shunsuke Takagi and Kei-ichi Watanabe},
journal= {arXiv preprint arXiv:math/0212340},
year = {2007}
}
Comments
12 pages, AMS-LaTeX; v.2: minor changes, to appear in Trans. Amer. Math. Soc