#### Vol. 279, No. 1-2, 2015

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Generic stabilisers for actions of reductive groups

### Benjamin Martin

Vol. 279 (2015), No. 1-2, 397–422
##### 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
Primary: 14L30
Secondary: 20G15