Compact complex manifolds with numerically effective cotangent bundles
type: Item
instance of: scholarly article
title: Compact complex manifolds with numerically effective cotangent bundles
zbMATH Open document ID: 0918.32011
author: Henrik Kratz
published in: Documenta Mathematica
publication date: 1998-04-14T00:00:00Z
full work available at URL: https://eudml.org/doc/229774
full work available at URL: vol-02.html
review text: Summary: We prove that a projective manifold of dimension \(n=2\) or 3 and Kodaira dimension 1 has a numerically effective cotangent bundle if and only if the Iitaka fibration is almost smooth, i.e. the only singular fibres are multiples of smooth elliptic curves \((n = 2)\) resp. multiples of smooth Abelian or hyperelliptic surfaces \((n = 3)\). In the case of a threefold which is fibred over a rational curve the proof needs an extra assumption concerning the multiplicities of the singular fibres. Furthermore, we prove the following Theorem: let \(X\) be a complex manifold which is hyberbolic with respect to the Carathéodory-Reiffen-pseudometric, then any compact quotient of \(X\) has a numerically effective cotangent bundle.
Mathematics Subject Classification ID: 32J18
Mathematics Subject Classification ID: 32J27
Mathematics Subject Classification ID: 32Q45
zbMATH DE Number: 1139207
zbMATH Keywords: numerically effective cotangent bundles
zbMATH Keywords: compact complex manifolds
zbMATH Keywords: numerically effective cotangent bundle
zbMATH Keywords: Iitaka fibration
zbMATH Keywords: Carathéodory-Reiffen-pseudometric
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1139207