English

Infinite transitivity and polynomial vector fields

Algebraic Geometry 2026-05-21 v1

Abstract

We prove that for many pairs H1,H2H_1, H_2 of root subgroups of the automorphism group Aut(C2)\text{Aut}(\mathbb{C}^2) the diagonal action of the group generated by H1,H2H_1, H_2 on (C2)m(\mathbb{C}^2)^m has an open orbit for any positive integer mm. 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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Cite

@article{arxiv.2605.20480,
  title  = {Infinite transitivity and polynomial vector fields},
  author = {Rafael B. Andrist and Ivan Arzhantsev},
  journal= {arXiv preprint arXiv:2605.20480},
  year   = {2026}
}

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13 pages