Niveau: Supérieur, Doctorat, Bac+8
Introduction to actions of algebraic groups Michel Brion Abstract. These notes present some fundamental results and examples in the theory of al- gebraic group actions, with special attention to the topics of geometric invariant theory and of spherical varieties. Their goal is to provide a self-contained introduction to more advanced lectures. Introduction These notes are based on lectures given at the conference “Hamiltonian actions: invariants and classification” (CIRM Luminy, April 6 - April 10, 2009). They present some fundamental results and examples in the theory of algebraic group actions, with special attention to the topics of geometric invariant theory and of spherical varieties. Geometric invariant theory provides very powerful tools for constructing and studying moduli spaces in algebraic geometry. On the other hand, spherical varieties form a remarkable class of algebraic varieties with algebraic group actions. They generalize several important subclasses such as toric varieties, flag varieties and symmetric varieties, and they satisfy many stability and finite- ness properties. The classification of spherical varieties by combinatorial invariants is an active research domain, and one of the main topics of the conference. The goal of these notes is to provide a self-contained introduction to more advanced lectures by Paolo Bravi, Ivan Losev and Guido Pezzini on spherical and wonderful varieties, and by Chris Woodward on geometric invariant theory and its relation to symplectic reduction. Here is a brief overview of the contents.
- c?
- any algebraic
- invariant theory
- group
- elements yields
- open subset
- any closed
- let c?
- algebraic group
- actions ?