Stable affine models for algebraic group actions

Zinovy Reichstein, Nikolaus Vonessen

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish
Pages (from-to)563-568
Number of pages6
JournalJournal of Lie Theory
Issue number2
StatePublished - 2004


  • Affine model
  • Algebraic group
  • Group action
  • Stable action


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