English

Closed H-orbits in G-varieties

Group Theory 2016-04-06 v2 Algebraic Geometry

Abstract

Let G be a linear algebraic group, H a subgroup of G and X a G-variety. This paper explores the connection between G-orbits and H-orbits in X, concentrating in particular on the question of when we have the implications G.x closed in X implies H.x closed in X, and vice versa. Some of the general results found in this paper are then used in the special case where G and H are reductive and X is affine to extend two classical results of Luna from characteristic zero to arbitrary characteristic.

Keywords

Cite

@article{arxiv.1211.0885,
  title  = {Closed H-orbits in G-varieties},
  author = {Michael Bate},
  journal= {arXiv preprint arXiv:1211.0885},
  year   = {2016}
}

Comments

The contents of this note have been incorporated and extended in the paper arXiv:1604.00924 of the author with H. Geranios and B. Martin

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