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Arkiv för Matematik


Infinite transitivity and special automorphisms1
Pub. online: 5 September 2023      Type: Research Article     

1 The research was supported by the grant RSF-DFG 16-41-01013.
Received
28 October 2016
Revised
14 May 2017
Published
5 September 2023

Abstract

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 Ga- or Gm-action. Moreover, 2-transitivity of the automorphism group implies infinite transitivity.

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© 2018 by Institut Mittag-Leffler. All rights reserved

Keywords
quasiaffine variety automorphism transitivity torus action rigidity

MSC
14J50 (primary) 14M17 (primary) 13A50 (secondary) 14L30 (secondary) 14R20 (secondary)

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