Closed Orbits and uniform S-instability in Geometric Invariant Theory

Details Closed Orbits and uniform S-instability in Geometric Invariant Theory Closed Orbits and uniform S-instability in Geometric Invariant Theory

2009-04-30

arxiv.org/abs/0904.4853v4

Mathematics

Algebraic Geometry

30 pages; expanded version; small suggestions by referee incorporated; final version, to appear in Trans. AMS

Scientific paper

In this paper we consider various problems involving the action of a reductive group $G$ on an affine variety $V$. We prove some general rationality results about the $G$-orbits in $V$. In addition, we extend fundamental results of Kempf and Hesselink regarding optimal destabilizing parabolic subgroups of $G$ for such general $G$-actions. We apply our general rationality results to answer a question of Serre concerning the behaviour of his notion of $G$-complete reducibility under separable field extensions. Applications of our new optimality results also include a construction which allows us to associate an optimal destabilizing parabolic subgroup of $G$ to any subgroup of $G$. Finally, we use these new optimality techniques to provide an answer to Tits' Centre Conjecture in a special case.

Affiliated with

Also associated with

No associations

Rating

Closed Orbits and uniform S-instability in Geometric Invariant Theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Closed Orbits and uniform S-instability in Geometric Invariant Theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Closed Orbits and uniform S-instability in Geometric Invariant Theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-443699