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

Part of: (Co)homology theory Holomorphic fiber spaces

Published online by Cambridge University Press:  27 August 2014

Junyan Cao
Junyan Cao*
Affiliation:
KIAS, 85 Hoegiro, Dongdaemun-gu, Seoul 130-722, Republic of Korea email junyan@kias.re.kr, jycao136@yahoo.com
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Abstract

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

Keywords

vanishing theoremcompact Kähler manifoldsNadel vanishing theorempseudo-effective line bundle

MSC classification

Primary: 32L20: Vanishing theorems 14F17: Vanishing theorems
Type
Research Article
Information
Compositio Mathematica , Volume 150 , Issue 11 , November 2014 , pp. 1869 - 1902
Copyright
© The Author 2014 

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