Linear systems on quasi-abelian varieties
type: Item
instance of: scholarly article
title: Linear systems on quasi-abelian varieties
zbMATH Open document ID: 0846.14028
DOI: 10.1007/BF01446625
author: F. Capocasa
author: Fabrizio Catanese
published in: Mathematische Annalen
publication date: 1996-09-26T00:00:00Z
full work available at URL: https://eudml.org/doc/165287
review text: The study of periodic meromorphic functions by the authors [Acta Math. 166, No. 1/2, 27-68 (1991; Zbl 0719.32005)] led to the definition of Cousin quasi-tori. The Cousin quasi-tori admitting a positive line bundle (or equivalently admitting the structure of a quasi-projective algebraic variety) are called quasi-abelian varieties. In these terms abelian varieties are exactly the compact quasi-abelian varieties. Suppose \(X\) is a quasi-abelian variety and \(L\) is a positive line bundle on \(X\). It is shown that for non-compact \(X\) the vector space \(H^0 (X,L)\) is infinite dimensional. Moreover the following Lefschetz type results are proven: \(H^0 (X, L^n)\) is base point free if \(n \geq 2\), and \(H^0 (X, L^n)\) gives a projective embedding if \(n \geq 3\). Also the theorem of Ohbuchi generalizes to quasi-abelian varieties: If \((X,L)\) admits no principally polarized abelian variety as factor, then \(H^0 (X,L^2)\) gives a projective embedding of \(X\).
Mathematics Subject Classification ID: 14K20
Mathematics Subject Classification ID: 32A20
Mathematics Subject Classification ID: 32L10
Mathematics Subject Classification ID: 14F25
Mathematics Subject Classification ID: 14C20
zbMATH DE Number: 734585
zbMATH Keywords: periodic meromorphic functions
zbMATH Keywords: Cousin quasi-tori
zbMATH Keywords: quasi-abelian varieties
zbMATH Keywords: projective embedding
reviewed by: Christina Birkenhake
MaRDI profile type: Publication
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cites work: Line bundles on toroidal groups.
OpenAlex ID: W1963748152
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description: scientific article; zbMATH DE number 734585