Generic stabilisers for actions of reductive groups

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In this paper we prove some results about properties of generic stabilisers. Most previous work in this area has dealt with affine varieties and/or fields of characteristic zero only. Our results hold for quasi-projective varieties and in arbitrary characteristic, although in some cases we get stronger results in characteristic zero. We need no assumptions on the existence of or properties of closed orbits, and we allow G to be non-connected.
Original languageEnglish
Pages (from-to)397-422
Number of pages26
JournalPacific Journal of Mathematics
Issue number1-2
Publication statusPublished - 21 Dec 2015


  • Quasiprojective GG-varieties
  • generic stabilisers
  • principal orbit type
  • GG-complete reducibility


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