Commutative algebraic groups and intersections of quadrics
type: Item
instance of: scholarly article
title: Commutative algebraic groups and intersections of quadrics
zbMATH Open document ID: 0544.14028
DOI: 10.1007/BF01455973
author: Herbert Lange
author: Friedrich Knop
published in: Mathematische Annalen
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/163916
review text: Let E be a commutative, connected algebraic group over an algebraically closed field k and \(0\to G\to E\to^{\pi}A\to 0\) the canonical exact sequence with a connected linear group G and an abelian variety A. (The assumption on k should be added to the paper.) Each equivariant completion \(\bar G\) of G induces a completion \(\bar E:=E\times^ G\bar G\) of E and a G-linearized linebundle L on \(\bar G\) induces a linebundle E(L) on \(\bar E\). The purpose of the paper is to give criteria when a linebundle of the form \(E(L)\otimes \pi^*(N)\quad(N\in Pic A)\) defines a projectively normal embedding of \(\bar E\) into projective space and whether the image is an intersection of quadrics. Then the results are specialized to the case when \(\bar G\) is a product of projective spaces. In this section all equivariant completions \(\bar G\) are determined where \(\bar G\) is isomorphic to a projective space.
Mathematics Subject Classification ID: 14L10
Mathematics Subject Classification ID: 14E25
zbMATH DE Number: 3865483
zbMATH Keywords: completion of algebraic group
zbMATH Keywords: projectively normal embedding
zbMATH Keywords: intersection of quadrics
MaRDI profile type: Publication
cites work: Zero estimates on group varieties. I
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description: scientific article; zbMATH DE number 3865483