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arXiv · 2605.20480

Infinite transitivity and polynomial vector fields

Rafael B. Andrist·Ivan Arzhantsev
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Abstract

We prove that for many pairs $H_1, H_2$ of root subgroups of the automorphism group $\text{Aut}(\mathbb{C}^2)$ the diagonal action of the group generated by $H_1, H_2$ on $(\mathbb{C}^2)^m$ has an open orbit for any positive integer $m$. The result is based on the study of the Lie algebra of polynomials in two variables with the standard Poisson bracket.

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Rafael B. Andrist, Ivan Arzhantsev. 2026-05-19. Infinite transitivity and polynomial vector fields. https://arxiv.org/abs/2605.20480

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