{
  "id": "1707.02563",
  "version": "v1",
  "published": "2017-07-09T11:46:59.000Z",
  "updated": "2017-07-09T11:46:59.000Z",
  "title": "On automorphisms of Enriques surfaces and their entropy",
  "authors": [
    "Yuya Matsumoto",
    "Hisanori Ohashi",
    "Sławomir Rams"
  ],
  "comment": "16 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Consider an arbitrary automorphism of an Enriques surface with its lift to the covering K3 surface. We prove a bound of the order of the lift acting on the anti-invariant cohomology sublattice of the Enriques involution. We use it to obtain some mod 2 constraint on the original automorphism. As an application, we give a necessary condition for Salem numbers to be dynamical degrees on Enriques surfaces and obtain a new bound on the minimal value. In the Appendix, we give a complete list of Salem numbers that potentially could be the minimal dynamical degree on Enriques surfaces and for which the existence of geometric automorphisms is unknown.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-09T11:46:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J28",
      "14J50",
      "37B40"
    ],
    "keywords": [
      "enriques surface",
      "salem numbers",
      "anti-invariant cohomology sublattice",
      "covering k3 surface",
      "enriques involution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}