An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities

Abstract

The purpose of this paper is to establish an injectivity theorem generalized to pseudo-effective line bundles with transcendental (non-algebraic) singular hermitian metrics and multiplier ideal sheaves. As an application, we obtain a Nadel type vanishing theorem. For the proof, we study the asymptotic behavior of the harmonic forms with respect to a family of regularized metrics, and give a method to obtain L2-estimates of solutions of the dbar-equation by using the de Rham-Weil isomorphism between the dbar-cohomology and the check{C}ech cohomology.

31pages, to appear in J. Algebraic Geom, essentially the same as v1, v4: completely revised version

References in corpus (6)

• Introduction to the log minimal model program for log canonical pairs
• The openness conjecture for plurisubharmonic functions
• Numerical dimension and a Kawamata-Viehweg-Nadel type vanishing theorem on compact Kähler manifolds
• Strong openness conjecture for plurisubharmonic functions
• An Injectivity Theorem
• Versions of injectivity and extension theorems

Cited by in corpus (8)

• Effectiveness of Demailly's strong openness conjecture and related problems
• Numerical dimension and a Kawamata-Viehweg-Nadel type vanishing theorem on compact Kähler manifolds
• Strong openness conjecture and related problems for plurisubharmonic functions
• Strong openness of multiplier ideal sheaves and optimal $L^2$ extension
• Injectivity theorem for pseudo-effective line bundles and its applications
• A Nadel vanishing theorem for metrics with minimal singularities on big line bundles
• Versions of injectivity and extension theorems
• Asymptotic estimate of cohomology groups valued in pseudo-effective line bundles