Lecturer: Michel Brion
The course will provide an introduction to linear algebraic groups and their actions on algebraic varieties. The main aim is to prove a fundamental result of Sumihiro: let X be a normal variety equipped with an action of a connected linear algebraic group G, then every point x of X admits an open G-stable neighborhood U_x, equivariantly isomorphic to a G-stable subvariety of some projective space on which G acts linearly. If G is a (split) torus, then each U_x may be taken affine.
References:
Michel Brion, Linearization of algebraic groups actions . Available at https://www-fourier.ujf-grenoble.fr/~mbrion/lin_rev.pdf