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A Kawamata-Viehweg Vanishing Theorem on compact Kahler manifolds

Jean-Pierre Demailly·Thomas Peternell
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Abstract

We prove a Kawamata-Viehweg vanishing theorem on a normal compact Kahler space X: if L is a nef line bundle with numerical dimension at least equal to 2, then the q-th cohomology group of K_X+L vanishes for q at least equal to the dimension of X minus 1. As an application, a special case of the abundance conjecture for minimal Kahler threefolds is proven: if X is a minimal Kahler threefold (in the usual sense that K_X is nef), then the Kodaira dimension kappa(X) is nonnegative.

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Jean-Pierre Demailly, Thomas Peternell. 2002-08-03. A Kawamata-Viehweg Vanishing Theorem on compact Kahler manifolds. https://arxiv.org/abs/math/0208021

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