G-birational rigidity of the projective plane

Abstract

Given a surface S and a finite group G of automorphisms of S, consider the birational maps S⤏ S′ that commute with the action of G. This leads to the notion of a G-minimal variety. A natural question arises: for a fixed group G, is there a birational G-map between two different G-minimal surfaces? If no such map exists, the surface is said to be G-birationally rigid. This paper determines the G-rigidity of the projective plane for every finite subgroup G⊂ PGL 3(C). © 2018, Springer International Publishing AG, part of Springer Nature.