Holomorphic vector bundles on non-algebraic tori of dimension 2
type: Item
instance of: scholarly article
title: Holomorphic vector bundles on non-algebraic tori of dimension 2
zbMATH Open document ID: 1167.14026
author: Koichi Kurihara
author: Kōta Yoshioka
published in: Manuscripta Mathematica
publication date: 2008-07-01T00:00:00Z
review text: The authors prove the following result: Theorem 0.1. Let \(X\) be a non-algebraic complex torus of dimension 2. Let \(E\) be a topological vector bundle of rank \(r\) over \(X\). Then \(E\) has a holomorphic structure if and only if \(c_{1}(E)\in \text{NS}(X)\) and \(\Delta(E)\geq0\). The case \(r=2\) was proved by \textit{M. Toma} [Math. Z. 232, No. 3, 511--525 (1999; Zbl 0945.32007)]. A similar result is proved in this paper for non-algebraic \(K3\)-surfaces.
reviewed by: Vasile Brînzănescu
Mathematics Subject Classification ID: 14J60
Mathematics Subject Classification ID: 14D20
zbMATH DE Number: 5294768
zbMATH Keywords: non-algebraic 2-tori
zbMATH Keywords: non-algebraic K3-surfaces
zbMATH Keywords: holomorphic vector bundles
zbMATH Keywords: Chern classes
MaRDI profile type: Publication
full work available at URL: s00229-008-0169-8
OpenAlex ID: W2052083377
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DOI: 10.1007/S00229-008-0169-8
description: scientific article; zbMATH DE number 5294768