Fibrations of compact Kähler manifolds in terms of cohomological properties of their fundamental groups
type: Item
instance of: scholarly article
title: Fibrations of compact Kähler manifolds in terms of cohomological properties of their fundamental groups
zbMATH Open document ID: 0986.53023
author: Ngaiming Mok
publication date: 2000-05-17T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75431
review text: If \(X\) denotes a compact Kähler manifold whose fundamental group is \(\Gamma\), the author considers some fibration theorems with conditions on the first cohomology groups of \(\Gamma\) with respect to unitary representations in complex Hilbert spaces. Thus, if for some unitary representation \(\Phi\) of \(\Gamma\) the first cohomology group \(H^{1}(\Gamma, \Phi)\) does not vanish, then either \(X\) is of general type or for some unramified finite cover of \(X\) there exists a holomorphic fibration of \(X\) over a complex compact torus or for some nonsingular Kähler modification of \(X\), there exists a holomorphic fibration \(\sigma\) with positive-dimensional fibers over a projective manifold of logarithmic general type with respect to the multiplicity locus of \(\sigma\). The author's method allows to obtain also some other results among which an interesting result on algebraic dimensions of compact Kähler manifolds.
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 37F75
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 58A14
Mathematics Subject Classification ID: 14D06
zbMATH DE Number: 1448494
zbMATH Keywords: compact Kähler manifolds
zbMATH Keywords: holomorphic fibration
zbMATH Keywords: foliation
zbMATH Keywords: harmonic maps and forms
reviewed by: Eugen Pascu
MaRDI profile type: Publication
OpenAlex ID: W2052766264
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DOI: 10.5802/AIF.1767
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 1448494