On the numerically effective compact Kähler manifolds of Ricci class
type: Item
instance of: scholarly article
title: On the numerically effective compact Kähler manifolds of Ricci class
zbMATH Open document ID: 0946.53037
DOI: 10.1016/S0007-4497(98)80078-X
author: Mihai Păun
published in: Bulletin des Sciences Mathématiques
publication date: 1998-06-02T00:00:00Z
review text: The author proves that, if \(X\) is a compact Kähler manifold of dimension \(n\), with the bundle \(K_X^{-1}\) numerically effective, then \(h^1(X,{\mathcal O}_X)\leq n\). Moreover, if \(\Gamma \) is a subgroup of the fundamental group of \(X\) generated by a finite number of elements, they prove that then there exists its normal subgroup \(\Gamma _1\) of finite index generated by at most \(4^{2n}+1\) elements. Here, the bundle \(L\) is numerically effective one if for each \(\varepsilon >0\) there exists a metric \(h_{\varepsilon }\) on \(L\) such that \(\Theta _{h_{\varepsilon }}(L)\geq -\varepsilon \omega\), where \(\omega \) is a fixed Hermitian metric on \(X\) and \(L\rightarrow X\) is a holomorphic bundle.
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 57R20
zbMATH DE Number: 1140252
zbMATH Keywords: numerically effective Ricci class
zbMATH Keywords: Kähler manifold
zbMATH Keywords: numerically effective bundle
reviewed by: Neda Bokan
MaRDI profile type: Publication
cites work: Q4151333
cites work: Projective manifolds whose tangent bundles are numerically effective
cites work: The splitting theorem for manifolds of nonnegative Ricci curvature
cites work: Q4692745
cites work: Q4294359
cites work: Q4285666
cites work: Q4880508
cites work: Q4747183
cites work: Variétés kähleriennes et premiere classe de Chern
cites work: Q2550561
description: scientific article; zbMATH DE number 1140252