A note on the normal generation of ample line bundles on abelian varieties
type: Item
instance of: scholarly article
title: A note on the normal generation of ample line bundles on abelian varieties
zbMATH Open document ID: 0699.14022
author: Akira Ohbuchi
published in: Proceedings of the Japan Academy. Series A
publication date: 1988-01-01T00:00:00Z
review text: Let k be an algebraically closed field, let A be an abelian variety defined over k and let L be an ample line bundle on A.- Our purpose is to give a condition for the normal generation of \(L^{\otimes 2}\). The result is as follows: Theorem. If char(k)\(\neq 2\) and L is a symmetric ample line bundle, then \(L^{\otimes 2}\) is normally generated if and only if the origin of A is not contained in \(Bs| L\otimes P_{\alpha}|\) for any \(\alpha \in \hat A_ 2=\{\alpha \in \hat A; 2\alpha =0\}\) where \(\hat A\) is the dual abelian variety of A, P is the Poincaré bundle on \(A\times \hat A\), \(P_{\alpha}=P_{A\times \{\alpha \}}\) for \(\alpha\in \hat A\) and \(Bs| L\otimes P_{\alpha}|\) is the set of all base points of \(L\otimes P_{\alpha}\).
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14K05
Mathematics Subject Classification ID: 14C20
zbMATH DE Number: 4146117
zbMATH Keywords: normal generation of ample line bundles
zbMATH Keywords: abelian variety
reviewed by: N. Mohan Kumar
MaRDI profile type: Publication
full work available at URL: pjaa.64.119
OpenAlex ID: W2070899950
cites work: Q5628266
cites work: Theta Relations and Projective Normality of Abelian Varieties
cites work: Some remarks on ample line bundles on abelian varieties
cites work: A note on the projective normality of special line bundles on abelian varieties
cites work: On projective normality of abelian varieties
cites work: On projective normality of abelian varieties. II
DOI: 10.3792/PJAA.64.119
description: scientific article; zbMATH DE number 4146117