{
  "id": "2007.06519",
  "version": "v1",
  "published": "2020-07-13T17:23:43.000Z",
  "updated": "2020-07-13T17:23:43.000Z",
  "title": "An integral version of Zariski decompositions on normal surfaces",
  "authors": [
    "Makoto Enokizono"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We show that any pseudo-effective divisor on a normal surface decomposes uniquely into its \"integral positive\" part and \"integral negative\" part, which is an integral analog of Zariski decompositions. As an application, we give a generalization of the Kawamata-Viehweg vanishing, Ramanujam's 1-connected vanishing and Miyaoka's vanishing theorems on surfaces. By using this vanishing result, we give a simple proof of Reider-type theorems including the log surface case and the relative case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-13T17:23:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C20",
      "14F17"
    ],
    "keywords": [
      "zariski decompositions",
      "integral version",
      "normal surface decomposes",
      "log surface case",
      "miyaokas vanishing theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}