On normal generation of line bundles on abelian threefolds
type: Item
instance of: scholarly article
title: On normal generation of line bundles on abelian threefolds
zbMATH Open document ID: 0956.14003
author: Elena Rubei
published in: Kodai Mathematical Journal
publication date: 1999-12-02T00:00:00Z
review text: An ample line bundle \(L\) on a projective variety is called ``normally generated'' if \(L\) is very ample and the corresponding projective embedding is projectively normal. According to a theorem of Koizumi an ample line bundle of type \((d_1,\dots,d_g)\) on an abelian variety \(X\) of dimension \(g\) is normally generated if only \(d_1\geq 3\). \textit{A. Ohbuchi} [Proc. Japan Acad., Ser. A 64, No. 4, 119-120 (1988; Zbl 0699.14022)] gave a criterion for an ample line bundle of type \((2,d_2,\dots,d_g)\) on \(X\) to be normally generated. In the present paper this criterion is exploited to determine explicitly, with the exception of some geometrical situations, which line bundles of type \((2,d_2, d_3)\) on an abelian threefold are normally generated. The main tool for the proof is a result of \textit{C. Birkenhake}, \textit{H. Lange} and \textit{S. Ramanan} [Manuscr. Math. 81, No. 3-4, 299-310 (1993; Zbl 0807.14030)] on global generation of line bundles on abelian threefolds. This result is also slightly generalized.
reviewed by: Herbert Lange
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14K05
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14J30
zbMATH DE Number: 1333296
zbMATH Keywords: projective normality of ample line bundle
zbMATH Keywords: abelian threefold
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138043985
OpenAlex ID: W2084322974
cites work: Primitive line bundles on abelian threefolds
cites work: Q4043308
cites work: Theta Relations and Projective Normality of Abelian Varieties
cites work: Q4023939
cites work: Varieties Defined by Quadratic Equations
cites work: Some remarks on ample line bundles on abelian varieties
cites work: A note on the normal generation of ample line bundles on abelian varieties
cites work: Q3842696
DOI: 10.2996/KMJ/1138043985
description: scientific article; zbMATH DE number 1333296