{
  "id": "1701.00580",
  "version": "v1",
  "published": "2017-01-03T04:23:46.000Z",
  "updated": "2017-01-03T04:23:46.000Z",
  "title": "On an Enriques surface associated with a quartic Hessian surface",
  "authors": [
    "Ichiro Shimada"
  ],
  "comment": "35 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We present several algorithmic methods to investigate the geometry of a complex Enriques surface by computation on the N\\'eron-Severi lattices of the Enriques surface and of its covering K3 surface. We apply them to an Enriques surface Y whose \\'etale double cover X is birational to a general quartic Hessian surface. Using the result on the automorphism group of X due to Dolgachev and Keum, we obtain a finite presentation of the automorphism group of Y. This automorphism group is compared with the automorphism group of the generic Enriques surface. A fundamental domain of the action of the automorphism group on the nef cone of Y is described explicitly. The list of elliptic fibrations on Y and the list of combinations of rational double points that can appear on a surface birational to Y are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-03T04:23:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J28"
    ],
    "keywords": [
      "automorphism group",
      "general quartic hessian surface",
      "complex enriques surface",
      "generic enriques surface",
      "algorithmic methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}