Ivan Arzhantsev, Mikhail Zaidenberg
Published 2021-11-12, updated 2022-11-11Version 3
A theorem of Cantat and Urech says that an analog of the classical Tits alternative holds for the group of birational automorphisms of a compact complex Kaehler surface. We established in our previous paper the following Tits-type alternative: if X is a toric affine variety and G is a subgroup of Aut(X) generated by a finite set of unipotent subgroups normalized by the acting torus then either G contains a nonabelian free subgroup or G is a unipotent affine algebraic group. In the present paper we extend the latter result to any group G of automorphisms of a complex affine surface generated by a finite collection of unipotent algebraic subgroups. It occurs that either G contains a nonabelian free subgroup or G is a metabelian unipotent algebraic group.
Comments: 16 pages; extended by an alternative, short proof of the main theorem valid over any algebraically closed field of characteristic zero. To appear in: Proc. Amer. Math. Soc
Jordan groups and algebraic surfaces
Topics in group schemes and surfaces in positive characteristic
Algebraic surfaces with quotient singularities - including some discussion on automorphisms and fundamental groups
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