Abstract
It is known that if the special automorphism group $\mathrm{SAut}(X)$ 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 $\mathbb{Aut}(X)$ to act infinitely transitively on $X$. We show that this is the case, provided $X$ admits a nontrivial $\mathbb{G}_a$ or $\mathbb{G}_m$-action. Moreover, $2$-transitivity of the automorphism group implies infinite transitivity.
Funding Statement
The author’s research was supported by the grant RSF-DFG 16-41-01013.
Citation
Ivan Arzhantsev. "Infinite transitivity and special automorphisms." Ark. Mat. 56 (1) 1 - 14, April 2018. https://doi.org/10.4310/ARKIV.2018.v56.n1.a1
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