Title: 

Infinitesimal symmetry in algebraic geometry: group schemes and del Pezzo surfaces

Abstract: 

Group schemes provide a refined notion of symmetry in positive characteristic: they detect infinitesimal structure invisible to the discrete automorphism group. Classical examples such as mu_p or alpha_p equip the trivial topological space with a non-trivial algebraic structure.

In this talk I will explain how this perspective can be used to classify weak and RDP del Pezzo surfaces admitting global vector fields, and how phenomena unique to small characteristic - such as non-lifting vector fields on rational double point singularities (RDPs) - can be illuminated using the group-scheme framework.

If time permits, I will outline applications and ongoing projects: towards higher-dimensional Fano varieties with infinite automorphism groups and (equivariant) compactifications of the affine plane.

https://www.unine.ch/math/seminaire-algebre-et-geometrie-de-neuchatel/