{
  "id": "0905.4141",
  "version": "v2",
  "published": "2009-05-26T09:02:56.000Z",
  "updated": "2011-02-07T23:53:26.000Z",
  "title": "String and dilaton equations for counting lattice points in the moduli space of curves",
  "authors": [
    "Paul Norbury"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove that the Eynard-Orantin symplectic invariants of the curve xy-y^2=1 are the orbifold Euler characteristics of the moduli spaces of genus g curves. We do this by associating to the Eynard-Orantin invariants of xy-y^2=1 a problem of enumerating covers of the two-sphere branched over three points. This viewpoint produces new recursion relations---string and dilaton equations---between the quasi-polynomials that enumerate such covers.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-02-07T23:53:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32G15",
      "30F30",
      "05A15"
    ],
    "keywords": [
      "counting lattice points",
      "moduli space",
      "dilaton equations",
      "orbifold euler characteristics",
      "eynard-orantin symplectic invariants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.4141N"
    }
  }
}