{
  "id": "2506.20524",
  "version": "v1",
  "published": "2025-06-25T15:10:17.000Z",
  "updated": "2025-06-25T15:10:17.000Z",
  "title": "On flexibility of trinomial varieties",
  "authors": [
    "Mikhail Ignatev",
    "Timofey Vilkin"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-06-25T15:10:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14R20",
      "14J50",
      "13A50",
      "13N15"
    ],
    "keywords": [
      "affine variety",
      "sufficient condition",
      "flexibility",
      "algebraic subgroups isomorphic",
      "arbitrary trinomial variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}