Algebraic Geometry Seminar

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Boundedness Properties for Birational Automorphisms

Speaker: Constantin Shramov, Higher School of Economics, Moscow

Location: Warren Weaver Hall 1302

Date: Thursday, April 16, 2015, 2:30 p.m.

Synopsis:

An old theorem due to H.Minkowski says that the orders of finite subgroups of the group GL_N(Q) are bounded by a constant that depends only on N. Another classical result (due to C.Jordan) is that for any finite subgroup G of GL_N(C) there is an abelian subgroup whose index in G is bounded by a constant that depends only on N. It is partially known and partially expected that birational automorphism groups of many varieties over Q and C, respectively, enjoy similar properties. I will survey the relevant results including low-dimensional cases, higher dimensional cases modulo standard conjectures of birational geometry, and explicit estimates for relevant constants.