A Kawamata-Viehweg Vanishing Theorem on Compact Kähler Manifolds

Abstract

We prove a Kawamata-Viehweg vanishing theorem on a normal compact Kähler space X: if L is a nef line bundle with L² ≠ 0, then H^>q(X,K_X+L) = 0 for q ≥ dim X − 1. As an application we complete a part of the abundance theorem for minimal Kähler threefolds: if X is a minimal Kähler threefold, then the Kodaira dimension κ(X) is nonnegative.