# Manchester Geometry Seminar 2015/2016

**Tuesday 22 September and Thursday 24 September. ** *The Frank Adams Room (Room 1.212), the Alan Turing Building. 4pm*
##
Automorphism Groups of Affine Varieties

Alexander Perepechko (Saint Petersburg State University)

`perepechko@gmail.com`

The affine algebraic surfaces admit quite various automorphism groups,
from finitely generated abelian groups to infinitely dimensional ones,
i.e. ind-groups, including amalgamated products of algebraic groups,
fundamental groups of graphs of groups, and even more complicated ones.

We will describe the arising automorphism groups with regard to the
number of additive group actions. We use the following technique. Each
automorphism of an affine surface induces a birational transformation of
its compactification that is represented by a sequence of blowups and
blowdowns with centers at the boundary divisor. Thus, we obtain
combinatorial transformations of the dual graph of the divisor and
describe through them the automorphism group up to a finite index.