{
  "id": "2101.05246",
  "version": "v1",
  "published": "2021-01-13T18:13:33.000Z",
  "updated": "2021-01-13T18:13:33.000Z",
  "title": "Automorphism groups of rational elliptic and quasi-elliptic surfaces in all characteristics",
  "authors": [
    "Igor Dolgachev",
    "Gebhard Martin"
  ],
  "comment": "38 pages, comments welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study the groups of automorphisms of rational algebraic surfaces that admit a relatively minimal pencil of curves of arithmetic genus one over an algebraically closed field of arbitrary characteristic. In particular, we classify such surfaces that admit non-trivial automorphisms that act trivially on the Picard group. As an application, we classify classical Enriques surfaces in characteristic $2$ that admit non-trivial numerically trivial automorphisms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-13T18:13:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J26",
      "14J27",
      "14J28",
      "14J50"
    ],
    "keywords": [
      "automorphism groups",
      "rational elliptic",
      "quasi-elliptic surfaces",
      "characteristic",
      "admit non-trivial numerically trivial automorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}