Jordan Groups, Abelian Varieties and Conic Bundles

A classical theorem of Jordan asserts that each finite subgroup of the complex general
linear group GL(n) is ``almost commutative": it contains a commutative normal subgroup 

with index bounded by an universal constant that depends only on n. We discuss an
analogue of this property for the groups of birational (and biregular) automorphisms of
complex algebraic varietiesand the groups of diffeomorphisms of real manifolds. 

 

This is a report on a joint work with Tatiana Bandman.