{
  "id": "2006.04457",
  "version": "v1",
  "published": "2020-06-08T10:18:37.000Z",
  "updated": "2020-06-08T10:18:37.000Z",
  "title": "On singularity types of del Pezzo surfaces with rational double points in positive characteristic",
  "authors": [
    "Tatsuro Kawakami",
    "Masaru Nagaoka"
  ],
  "comment": "12 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper, we prove that a pair of the minimal resolution of a del Pezzo surface with rational double points whose general anti-canonical member is smooth and its exceptional divisor lifts to the Witt ring. We also classify a del Pezzo surface with rational double points whose anti-canonical members are all singular. As a corollary, we determine all singularity types of del Pezzo surfaces with rational double points which only appear in positive characteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-08T10:18:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J26",
      "14J45",
      "14G17"
    ],
    "keywords": [
      "del pezzo surface",
      "rational double points",
      "singularity types",
      "positive characteristic",
      "exceptional divisor lifts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}