Infinite transitivity and polynomial vector fields
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911699975536640 |
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| author | Andrist, Rafael B. Arzhantsev, Ivan |
| author_facet | Andrist, Rafael B. Arzhantsev, Ivan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20480 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Infinite transitivity and polynomial vector fields Andrist, Rafael B. Arzhantsev, Ivan Algebraic Geometry Primary 14R10, 17B66, Secondary 14R20, 22E65, 32M17 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. |
| title | Infinite transitivity and polynomial vector fields |
| topic | Algebraic Geometry Primary 14R10, 17B66, Secondary 14R20, 22E65, 32M17 |
| url | https://arxiv.org/abs/2605.20480 |