Generic stabilisers for actions of reductive groups

Benjamin Martin

Vol. 279 (2015), No. 1-2, 397–422

DOI: 10.2140/pjm.2015.279.397

Abstract

Let $G$ be a reductive algebraic group over an algebraically closed field and let $V$ be a quasiprojective $G$-variety. We prove that the set of points $v\in V$ such that $dim\left(G_v\right)$ is minimal and $G_v$ is reductive is open. We also prove some results on the existence of principal stabilisers in an appropriate sense.

Keywords

Quasiprojective $G$-varieties, generic stabilisers, principal orbit type, $G$-complete reducibility

Mathematical Subject Classification 2010

Primary: 14L30

Secondary: 20G15

Milestones

Received: 8 June 2015

Revised: 24 August 2015

Accepted: 25 August 2015

Published: 21 December 2015