Conjugacy in Cremona Groups and the alpha-invariant of Tian

Andrew Wilson (U Glasgow)

Wednesday 24th April, 2013 16:00-17:00 204


The Cremona group is the group of birational automorphisms of projective n-space.  In dimension one there are no birational automorphisms that are not biregular.  In dimension two, the Cremona group is already large and complex and in higher dimensions our understanding is even poorer.  One step towards a holistic understanding of the structure of these higher dimensional Cremona groups is the ability to describe their conjugacy classes.  A modern approach to this is to consider rational varieties with a biregular group action and equivariant birational maps between them.  I'll talk about a method to determine conjugacy of subgroups in higher dimensional Cremona groups using the alpha-invariant of Tian.

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