{
  "id": "1010.4126",
  "version": "v1",
  "published": "2010-10-20T08:40:22.000Z",
  "updated": "2010-10-20T08:40:22.000Z",
  "title": "The asymptotic Weil-Petersson form and intersection theory on M_{g,n}",
  "authors": [
    "Norman Do"
  ],
  "comment": "22 pages",
  "categories": [
    "math.GT",
    "math.AG"
  ],
  "abstract": "Moduli spaces of hyperbolic surfaces with geodesic boundary components of fixed lengths may be endowed with a symplectic structure via the Weil-Petersson form. We show that, as the boundary lengths are sent to infinity, the Weil-Petersson form converges to a piecewise linear form first defined by Kontsevich. The proof rests on the observation that a hyperbolic surface with large boundary lengths resembles a graph after appropriately scaling the hyperbolic metric. We also include some applications to intersection theory on moduli spaces of curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-20T08:40:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32G15",
      "53D30",
      "14H10"
    ],
    "keywords": [
      "asymptotic weil-petersson form",
      "intersection theory",
      "linear form first",
      "hyperbolic surface",
      "large boundary lengths resembles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.4126D"
    }
  }
}