On flexibility of trinomial varieties
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912449760854016 |
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| author | Ignatev, Mikhail Vilkin, Timofey |
| author_facet | Ignatev, Mikhail Vilkin, Timofey |
| contents | Trinomial varieties are affine varieties given by a system of equations consisting of polynomials with three terms. Such varieties are total coordinate spaces of normal varieties with torus action of complexity one. For an affine variety $X$ we consider the subgroup $\mathrm{SAut}(X)$ of the automorphism group generated by all algebraic subgroups isomorphic to the additive group of the ground field. By definition, an affine variety is flexible if $\mathrm{SAut}(X)$ acts transitively on its regular locus. Gaifullin proved a sufficient condition for a trinomial hypersurface to be flexible. We give a generalization of his results, proving a sufficient condition to be flexible for an arbitrary trinomial variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20524 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On flexibility of trinomial varieties Ignatev, Mikhail Vilkin, Timofey Algebraic Geometry Commutative Algebra primary 14R20, 14J50, secondary 13A50, 13N15 Trinomial varieties are affine varieties given by a system of equations consisting of polynomials with three terms. Such varieties are total coordinate spaces of normal varieties with torus action of complexity one. For an affine variety $X$ we consider the subgroup $\mathrm{SAut}(X)$ of the automorphism group generated by all algebraic subgroups isomorphic to the additive group of the ground field. By definition, an affine variety is flexible if $\mathrm{SAut}(X)$ acts transitively on its regular locus. Gaifullin proved a sufficient condition for a trinomial hypersurface to be flexible. We give a generalization of his results, proving a sufficient condition to be flexible for an arbitrary trinomial variety. |
| title | On flexibility of trinomial varieties |
| topic | Algebraic Geometry Commutative Algebra primary 14R20, 14J50, secondary 13A50, 13N15 |
| url | https://arxiv.org/abs/2506.20524 |