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Journal of Lie Theory 14 (2004), No. 2, 563--568
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,

Nikolaus Vonessen
Dept. of Mathematical Sciences, University of Montana, Missoula MT 59812-0864, U.S.A.,

Let G be a reductive linear algebraic group defined over an algebraically closed base field k of characteristic zero. A G-variety is an algebraic variety with a regular action of G, defined over k. An affine G-variety is called stable if its points in general position have closed G-orbits. We give a simple necessary and sufficient condition for a G-variety to have a stable affine birational model.

Keywords: Algebraic group, group action, stable action, affine model.

MSC: 14L30.

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