Michel Brion: Infinitesimal automorphisms of algebraic curves

Abstract:

The objects of the talk are curves over a field of positive characteristic. Their automorphism groups have been extensively investigated, but their automorphism group schemes (in particular, their vector fields) are much less understood. An issue is that the classical identification between automorphisms of a normal projective curve and those of its function field does not extend to automorphism group schemes. The talk will introduce a notion of “equivariant normalization” as a partial remedy, and present some properties of equivariantly normal curves. These show up naturally in the classification of smooth projective surfaces in small characteristics.