The exactness of a general Skoda complex

Abstract

We show that a Skoda complex with a general plurisubharmonic weight function is exact if its 'degree' is sufficiently large. This answers a question of Lazarsfeld and implies that not every integrally closed ideal is equal to a multiplier ideal even if we allow general plurisubharmonic weights for the multiplier ideal, extending the result of Lazarsfeld and Lee \cite{LL}.

References added, exposition streamlined, to appear in Michigan Mathematical Journal

References in corpus (2)

• Local syzygies of multiplier ideals
• $L^2$ extension of adjoint line bundle sections

Cited by in corpus (2)

• Strong openness conjecture and related problems for plurisubharmonic functions
• A Nadel vanishing theorem for metrics with minimal singularities on big line bundles