Infinite transitivity and polynomial vector fields
Algebraic Geometry
2026-05-21 v1
Abstract
We prove that for many pairs of root subgroups of the automorphism group the diagonal action of the group generated by on has an open orbit for any positive integer . The result is based on the study of the Lie algebra of polynomials in two variables with the standard Poisson bracket.
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