Journal of Lie Theory EMIS ELibM Electronic Journals Journal of Lie Theory
Vol. 14, No. 2, pp. 563--568 (2004)

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Stable Affine Models for Algebraic Group Actions

Zinovy Reichstein and Nikolaus Vonessen

Zinovy Reichstein
Department of Mathematics
University of British Columbia
Vancouver, BC V6T 1Z2
Nikolaus Vonessen
Department of Mathematical Sciences
University of Montana
Missoula, MT 59812-0864

Abstract: 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.

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Electronic version published on: 1 Sep 2004. This page was last modified: 1 Sep 2004.

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