Infinite transitivity and special automorphisms

Ivan Arzhantsev National Research University Higher School of Economics

Algebraic Geometry mathscidoc:1912.43001

Arkiv for Matematik, 56, (1), 1 – 14, 2018
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.
quasiaffine variety, automorphism, transitivity, torus action, rigidity
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  title={Infinite transitivity and special automorphisms},
  author={Ivan Arzhantsev},
  booktitle={Arkiv for Matematik},
  pages={1 – 14},
Ivan Arzhantsev. Infinite transitivity and special automorphisms. 2018. Vol. 56. In Arkiv for Matematik. pp.1 – 14.
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