{
  "id": "0803.3008",
  "version": "v2",
  "published": "2008-03-20T15:20:49.000Z",
  "updated": "2008-03-26T18:45:08.000Z",
  "title": "A characterization of surfaces whose universal cover is the bidisk",
  "authors": [
    "Fabrizio Catanese",
    "Marco Franciosi"
  ],
  "comment": "12 pages, references added",
  "categories": [
    "math.AG",
    "math.CV"
  ],
  "abstract": "We show that the universal cover of a compact complex surface $X$ is the bidisk $\\HH \\times \\HH$, or $X$ is biholomorphic to $\\PP^1 \\times \\PP^1$, if and only if $K_X^2 > 0$ and there exists an invertible sheaf $\\eta$ such that $\\eta^2\\cong \\hol_X$ and $H^0(X, S^2\\Omega^1_X (-K_X) \\otimes \\eta) \\neq 0$. The two cases are distinguished by the second plurigenus, $P_2(X)\\geq 2$ in the former case, $P_2(X)= 0$ in the latter. We also discuss related questions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-03-26T18:45:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J25",
      "14J29"
    ],
    "keywords": [
      "universal cover",
      "characterization",
      "compact complex surface",
      "second plurigenus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.3008C"
    }
  }
}