Jordan property for automorphism groups of projective varieties

De-Qi Zhang

13 dec 2019 -- 11:00

Aula Tricerri, DiMaI, Firenze

Abstract.

Acentury ago, Camille Jordan proved that the complex general linear group GL_n(C) has the Jordan property: there is a Jordan constant C_n such that every finite subgroup H < GL_n(C) has an abelian subgroup H1 of index H:H1 < C_n. We show that every connected algebraic group G (which is not necessarily linear) has the Jordan property with the Jordan constant depending only on dim G, and that the full automorphism group Aut(X) of every projective variety X has the Jordan property. We will also mention recent results on the Jordan property of birational groups of algebraic varieties and automorphism groups of complex manifolds.