The cohomology of line bundles on non-primary Hopf manifolds
type: Item
instance of: scholarly article
title: The cohomology of line bundles on non-primary Hopf manifolds
zbMATH Open document ID: 1116.32014
author: Ning Gan
author: Xiangyu Zhou
publication date: 2007-06-07T00:00:00Z
review text: A Hopf manifold \(X\) is an \(n\)-dimensional compact complex manifold with \(W:= \mathbb {C}^n \backslash \{0\}\) as universal covering. Hence \(X = W/G\) with \(G\) a group. \(X\) is called primary if \(G = \mathbb {Z}\). Here the authors give an elementary method to compute the cohomology groups \(H^q(X,\Omega ^p_X(L))\), \(L\) a flat holomorphic line bundle, generalizing the case \(G = \mathbb {Z}\) done in [\textit{X. Y. Zhou}, Asian J. Math. 8, No. 1, 131--136 (2004; Zbl 1068.32013)] and the case \(G\) Abelian done in [\textit{X. Y. Zhou} and \textit{W. M. Liu}, Acta Math. Sin., Engl. Ser. 20, No. 4, 605--612 (2004; Zbl 1060.32006)].
reviewed by: E. Ballico
Mathematics Subject Classification ID: 32L10
Mathematics Subject Classification ID: 32J18
zbMATH DE Number: 5162305
zbMATH Keywords: non-primary Hopf manifold
zbMATH Keywords: Douady sequence
zbMATH Keywords: cohomology
zbMATH Keywords: line bundles
zbMATH Keywords: flat line bundle
zbMATH Keywords: Dolbeault cohomology
MaRDI profile type: Publication
full work available at URL: s10114-005-0721-3
OpenAlex ID: W1974341732
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DOI: 10.1007/S10114-005-0721-3
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5162305