{
  "id": "1607.03472",
  "version": "v1",
  "published": "2016-07-12T19:34:35.000Z",
  "updated": "2016-07-12T19:34:35.000Z",
  "title": "The automorphism group of a rigid affine variety",
  "authors": [
    "Ivan Arzhantsev",
    "Sergey Gaifullin"
  ],
  "comment": "10 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "An algebraic variety $X$ is rigid if it admits no nontrivial action of the additive group of the ground field. We prove that the automorphism group $\\text{Aut}(X)$ of a rigid affine variety contains a unique maximal torus $\\mathbb{T}$. If the grading on the algebra of regular functions $\\mathbb{K}[X]$ defined by the action of $\\mathbb{T}$ is pointed, the group $\\text{Aut}(X)$ is a finite extension of $\\mathbb{T}$. As an application, we describe the automorphism group of a rigid trinomial affine hypersurface and find all isomorphisms between such hypersurfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-12T19:34:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J50",
      "14R20",
      "13A50",
      "14L30"
    ],
    "keywords": [
      "automorphism group",
      "rigid affine variety contains",
      "rigid trinomial affine hypersurface",
      "unique maximal torus",
      "ground field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}