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Pré-Publication, Document De Travail Année : 2021

TITS-TYPE ALTERNATIVE FOR CERTAIN GROUPS ACTING ON ALGEBRAIC SURFACES

Résumé

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 [AZ21] the following Tits-type alternative: if X is a toric affine variety and G ⊂ Aut(X) is a subgroup 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.
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Dates et versions

hal-03427074 , version 1 (12-11-2021)
hal-03427074 , version 2 (02-12-2021)
hal-03427074 , version 3 (11-11-2022)

Identifiants

Citer

Ivan Arzhantsev, M Zaidenberg. TITS-TYPE ALTERNATIVE FOR CERTAIN GROUPS ACTING ON ALGEBRAIC SURFACES. 2021. ⟨hal-03427074v3⟩

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