{
  "id": "1004.1684",
  "version": "v2",
  "published": "2010-04-10T04:54:45.000Z",
  "updated": "2011-12-20T10:26:15.000Z",
  "title": "The Canonical Map and Horikawa Surfaces in Positive Characteristic",
  "authors": [
    "Christian Liedtke"
  ],
  "comment": "31 pages, only minor changes, mainly typos",
  "journal": "Int. Math. Res. Not. IMRN 2013, no. 2, 422-462",
  "categories": [
    "math.AG"
  ],
  "abstract": "We extend fundamental inequalities related to the canonical map of surfaces of general type to positive characteristic. Next, we classify surfaces on the Noether lines, i.e., even and odd Horikawa surfaces, in positive characteristic. We describe their moduli spaces and the subspaces formed by surfaces whose canonical maps are inseparable. Moreover, we compute their Betti-, deRham- and crystalline cohomology. Finally, we prove lifting to characteristic zero and show that the moduli spaces are topologically flat over the integers.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-12-20T10:26:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J29",
      "14J10"
    ],
    "keywords": [
      "positive characteristic",
      "canonical map",
      "moduli spaces",
      "odd horikawa surfaces",
      "general type"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.1684L"
    }
  }
}