A Nadel vanishing theorem for metrics with minimal singularities on big line bundles

Abstract

The purpose of this paper is to establish a Nadel vanishing theorem for big line bundles with multiplier ideal sheaves of singular metrics admitting an analytic Zariski decomposition (such as, metrics with minimal singularities and Siu's metrics). For this purpose, we apply the theory of harmonic integrals and generalize Enoki's proof of Koll'ar's injectivity theorem. Moreover we investigate the asymptotic behavior of harmonic forms with respect to a family of regularized metrics.

18pages, to appear in Adv. Math. 280 (2015), 188--207, v3: completely revised version

References in corpus (6)

• Effectiveness of Demailly's strong openness conjecture and related problems
• The openness conjecture for plurisubharmonic functions
• The diminished base locus is not always closed
• An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities
• Versions of injectivity and extension theorems
• Equivalence of plurisubharmonic singularities and Siu-type metrics

Cited by in corpus (5)

• Strong openness conjecture for plurisubharmonic functions
• Strong openness conjecture and related problems for plurisubharmonic functions
• Injectivity theorem for pseudo-effective line bundles and its applications
• Equivalence of plurisubharmonic singularities and Siu-type metrics
• Restricted volumes on Kähler manifolds