
Journal of Lie Theory 14 (2004), No. 2, 563568 Copyright Heldermann Verlag 2004 Stable Affine Models for Algebraic Group Actions Zinovy Reichstein Dept. of Mathematics, University of British Columbia, Vancouver BC, V6T 1Z2 Canada, reichst@math.ubc.ca Nikolaus Vonessen Dept. of Mathematical Sciences, University of Montana, Missoula MT 598120864, U.S.A., Nikolaus.Vonessen@umontana.edu Let G be a reductive linear algebraic group defined over an algebraically closed base field k of characteristic zero. A Gvariety is an algebraic variety with a regular action of G, defined over k. An affine Gvariety is called stable if its points in general position have closed Gorbits. We give a simple necessary and sufficient condition for a Gvariety to have a stable affine birational model. Keywords: Algebraic group, group action, stable action, affine model. MSC: 14L30. [FullTextpdf (138 KB)] for subscribers only. 