June 6, Wednesday, 15:30, room 211shinymath, · Categories: Без рубрики
Automorphisms of varieties, Cox rings and locally nilpotent derivations
We plan to consider automorphism groups of complex algebraic varieties. Groups which arise in this way are of quite different nature; compare, for example, the automorphsim groups of projective spaces, affine spaces and algebraic tori. We are going to discuss some approaches to the study of automorphsim groups.
Any connected linear algebraic group is generated by its maximal torus and one-parameter root subgroups. This observation was used by Demazure (1970) to describe the automorphism group of a compact toric variety. For affine varieties, torus actions correspond to gradings on the algebra of regular functions, while root subgroups are in bijection with homogeneous locally nilpotent derivations. The theory of Cox rings allows to reduce the study of automorphisms of a wide class of varieties to the affine case.