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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,
reichst@math.ubc.ca
Nikolaus Vonessen
Dept. of Mathematical Sciences, University of Montana, Missoula MT 59812-0864, 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 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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