{
  "id": "1903.07699",
  "version": "v1",
  "published": "2019-03-18T20:11:15.000Z",
  "updated": "2019-03-18T20:11:15.000Z",
  "title": "When is the automorphism group of an affine variety nested?",
  "authors": [
    "Alexander Perepechko",
    "Andriy Regeta"
  ],
  "comment": "9 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "For an affine algebraic variety $X$, we study the subgroup $\\mathrm{Aut}_{\\text{alg}}(X)$ of the group of regular automorphisms $\\mathrm{Aut}(X)$ of $X$ generated by all the connected algebraic subgroups. We prove that $\\mathrm{Aut}_{\\text{alg}}(X)$ is nested, i.e., is a direct limit of algebraic subgroups of $\\mathrm{Aut}(X)$, if and only if all the $\\mathbb{G}_a$-actions on $X$ commute. Moreover, we describe the structure of such a group $\\mathrm{Aut}_{\\text{alg}}(X)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-18T20:11:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14R05",
      "14R20",
      "14R25"
    ],
    "keywords": [
      "affine variety",
      "automorphism group",
      "affine algebraic variety",
      "regular automorphisms",
      "connected algebraic subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}