Real geometric invariant theory
Differential Geometry
2017-07-21 v3 Algebraic Geometry
Representation Theory
Abstract
For linear actions of real reductive Lie groups we prove the Kempf-Ness Theorem about closed orbits and the Kirwan-Ness Stratification Theorem of the null cone. Since our completely self-contained proof focuses strongly on geometric and analytic methods, essentially avoiding any deep algebraic result, it applies also to non-rational linear actions.
Cite
@article{arxiv.1701.00643,
title = {Real geometric invariant theory},
author = {Christoph Böhm and Ramiro A. Lafuente},
journal= {arXiv preprint arXiv:1701.00643},
year = {2017}
}
Comments
23 pages; v2: sections were completely reorganised, some proofs were rewritten and several typos fixed; v3: Fixed proof of Prop. 8.3, added Cor. 9.3, and some minor changes