Speaker: Michel Brion
Date: December 08, 2025
Affiliation: Université Grenoble Alpes, Institute Fourier

Abstract: A central result in algebraic geometry is Hironaka'stheorem : every variety $X$ over a field of characteristic zero has a resolution of singularities. Subsequent work showed that there even exists an equivariant resolution $X'$, that is, every action of an algebraic group $G$ on $X$ lifts to an action on $X'$. The latter result fails in positive characteristics, already for curves. The talk will present some general background, examples in positive characteristics, and finally a notion of equivariant regularity as a remedy to the failure of equivariant resolution.