On periodic functions of several complex variables. II: Reduction to the positive definite case
type: Item
instance of: scholarly article
title: On periodic functions of several complex variables. II: Reduction to the positive definite case
zbMATH Open document ID: 0788.32015
author: Yukitaka Abe
published in: Journal of the Mathematical Society of Japan
publication date: 1994-05-26T00:00:00Z
review text: The quotient complex manifold \(X=\mathbb{C}^ n/ \Gamma\), where \(\Gamma\) denotes a discrete subgroup, is called a toroidal group, if \(H^ 0(X,{\mathcal O}_ X)=\mathbb{C}\). The aim of the paper is to characterize those line bundles \(L\) on \(X\) which admit nontrivial holomorphic sections. The author gives some necessary conditions and finally reduces the question to the case of a positive line bundle on \(X\). Remark: Recently the problem has been solved by Copocasa and Catanese, who showed (preprint 1993) that every positive line bundle on a toroidal group admits nonzero holomorphic sections. [For part I of the paper see the author, Nagoya Math. J. 122, 83-114 (1991; Zbl 0749.32015)].
reviewed by: Herbert Lange
Mathematics Subject Classification ID: 32G20
zbMATH DE Number: 469050
zbMATH Keywords: toroidal group
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04510059
OpenAlex ID: W2149939056
DOI: 10.2969/JMSJ/04510059
description: scientific article; zbMATH DE number 469050