A Kawamata-Viehweg Vanishing Theorem on compact Kahler manifolds
Algebraic Geometry
2007-05-23 v1 Complex Variables
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.
Keywords
Cite
@article{arxiv.math/0208021,
title = {A Kawamata-Viehweg Vanishing Theorem on compact Kahler manifolds},
author = {Jean-Pierre Demailly and Thomas Peternell},
journal= {arXiv preprint arXiv:math/0208021},
year = {2007}
}
Comments
36 pages, Plain-TeX