Numerical dimension and a Kawamata-Viehweg-Nadel type vanishing theorem on compact Kähler manifolds

Abstract

Let $X$ be a compact Kähler manifold and let $(L,\phi )$ be a pseudo-effective line bundle on $X$. We first define a notion of numerical dimension of pseudo-effective line bundles with singular metrics, and then discuss the properties of this type numerical dimension. We finally prove a very general Kawamata-Viehweg-Nadel type vanishing theorem on an arbitrary compact Kähler manifold.

References in corpus (3)

• The openness conjecture for plurisubharmonic functions
• Extension of log pluricanonical forms from subvarieties
• An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities

Cited by in corpus (21)

• Effectiveness of Demailly's strong openness conjecture and related problems
• Strong openness conjecture for plurisubharmonic functions
• Strong openness conjecture and related problems for plurisubharmonic functions
• Strong openness of multiplier ideal sheaves and optimal $L^2$ extension
• An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities
• The closures of test configurations and algebraic singularity types
• Injectivity theorems with multiplier ideal sheaves and their applications
• Logarithmic vanishing theorems on compact Kähler manifolds I
• Extension of cohomology classes and holomorphic sections defined on subvarieties
• On a Bogomolov type vanishing theorem
• Asymptotic estimate of cohomology groups valued in pseudo-effective line bundles
• A Nadel-type vanishing theorem concerning the asymptotic multiplier ideal sheaf
• An eigenvalue estimate for the $\bar{\partial }$-Laplacian associated to a nef line bundle
• On the modified ideal sheaf
• Local Demailly-Bouche's holomorphic Morse inequalities
• Global generation and very ampleness for adjoint linear series
• A note on multiplier ideal sheaves on complex spaces with singularities
• On Junyan Cao's vanishing theorem for pseudoeffective line bundles
• Partial Okounkov bodies and Duistermaat--Heckman measures of non-Archimedean metrics
• Decreasing equisingular approximations with analytic singularities
• A generalization of Nadel vanishing theorem