The exactness of a general Skoda complex

Details The exactness of a general Skoda complex The exactness of a general Skoda complex

2010-07-04

arxiv.org/abs/1007.0551v1

Mathematics

Algebraic Geometry

Scientific paper

We show that a $q$-th Skoda complex with a general plurisubharmonic weight function is exact if $q$ is sufficiently large. Following work of Lazarsfeld and Lee, this implies that not every integrally closed ideal can be written as a multiplier ideal even if we allow nonalgebraic plurisubharmonic weights. This general case of the exactness uses a very different method from the algebraic case, due to the openness conjecture of Demailly and Koll\'ar.

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