English

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.

Keywords

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

R2 v1 2026-06-22T17:39:51.988Z