A vanishing theorem for semipositive line bundles over non-Kähler manifolds
type: Item
instance of: scholarly article
title: A vanishing theorem for semipositive line bundles over non-Kähler manifolds
zbMATH Open document ID: 0577.32031
author: Yum-Tong Siu
published in: Journal of Differential Geometry
publication date: 1984-01-01T00:00:00Z
review text: The main result is the following. Let M be a compact complex manifold and L be a Hermitian holomorphic line bundle on M. Suppose the curvature form of L being everywhere semipositive and being strictly positive outside a set of measure zero. Then \(H^ q(M,LK_ M)=0\) for \(q\geq 1\), where \(K_ M\) is the canonical line bundle of M. A characterization of Moišezon manifolds is given. Connections with the conjecture of Grauert-Riemenschneider and the eigenvalue conjecture are discussed, too.
Mathematics Subject Classification ID: 32L20
Mathematics Subject Classification ID: 32L10
Mathematics Subject Classification ID: 32J99
Mathematics Subject Classification ID: 32J15
zbMATH DE Number: 3923125
zbMATH Keywords: compact complex manifold
zbMATH Keywords: Hermitian holomorphic line bundle
zbMATH Keywords: curvature form
zbMATH Keywords: Moišezon manifolds
zbMATH Keywords: conjecture of Grauert-Riemenschneider
zbMATH Keywords: eigenvalue conjecture
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214438686
OpenAlex ID: W1480140700
Wikidata QID: Q115187786
DOI: 10.4310/JDG/1214438686
description: scientific article; zbMATH DE number 3923125