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Regular version of the site

Article

Infinite transitivity and special automorphisms

Arkiv for Matematik. 2018. Vol. 56. No. 1. P. 1-14.

It is known that if the special automorphism group SAut(X) of a quasiaffine variety X of dimension at least 2 acts transitively on X, then this action is infinitely transitive. In this paper we question whether this is the only possibility for the automorphism group Aut(X) to act infinitely transitively on X. We show that this is the case, provided X admits a nontrivial G_a- or G_m-action. Moreover, 2-transitivity of the automorphism group implies infinite transitivity.