Equivariant birational types and Burnside volume

Abstract

We introduce equivariant Burnside groups, new invariants in equivariant birational geometry, generalizing birational symbols groups for actions of finite abelian groups, due to Kontsevich, Pestun, and the second author, and study their properties.We establish a specialization map for the equivariant birational type of a smooth algebraic variety with an action of a finite group.As a consequence we obtain the equivariant specialization of birationality (Corollary 6.8):Ifare smooth and projective, with generically free actions of a finite group G and G-equivariantly birational generic fibers, then the special fibers are G-equivariantly birational.

Topics & Concepts