Seminar Algebra and Geometry: Tatiana Bandman (Bar Ilan)

Jordan groups and birational automorphisms of algebraic varieties

A group G  is called Jordan  if there is a positive integer J  = JG  such that every nite subgroup B  of G  contains a commutative subgroup A c B  such that A  is normal in B  and the index [B  : A ]<= J . There is no example of an algebraic variety with the non-Jordan automorphism group. It is known that the group of birational automorphisms Bir(X ) of a projective variety X  is Jordan if it is not uniruled and is not Jordan if X  is birational to the direct product of a projective space with an abelian variety. I will give an introduction to the topic and discuss the case when variety X  is a conic bundle over a non-uniruled variety Y  and is not birational to Y x P^1:  This is a joint work with Y. Zarhin.

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