تقرير
Closed Orbits and uniform S-instability in Geometric Invariant Theory
| العنوان: | Closed Orbits and uniform S-instability in Geometric Invariant Theory |
|---|---|
| المؤلفون: | Bate, M., Martin, B., Roehrle, G., Tange, R. |
| سنة النشر: | 2009 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, Mathematics - Group Theory, 20G15, 14L24, 20E42 |
| الوصف: | 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. Comment: 30 pages; expanded version; small suggestions by referee incorporated; final version, to appear in Trans. AMS |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/0904.4853 |
| رقم الأكسشن: | edsarx.0904.4853 |
| قاعدة البيانات: | arXiv |
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