{
  "id": "0902.3839",
  "version": "v2",
  "published": "2009-02-23T02:40:00.000Z",
  "updated": "2014-03-17T23:47:17.000Z",
  "title": "Gauss-Bonnet-Chern theorem on moduli space",
  "authors": [
    "Zhiqin Lu",
    "Michael R. Douglas"
  ],
  "comment": "Final version, Journal ref added",
  "journal": "Math. Ann., 357, 2013, 469-511",
  "doi": "10.1007/s00208-013-0907-4",
  "categories": [
    "math.DG",
    "hep-th",
    "math.AG"
  ],
  "abstract": "In this paper, we proved the Gauss-Bonnet-Chern theorem on moduli space of polarized Kahler manifolds. Using our results, we proved the rationality of the Chern-Weil forms (with respect to the Weil-Petersson metric) on CY moduli. As an application in physics, by the Ashok-Douglas theory, counting the number of flux compactifications of the type IIb string on a Calabi-Yau threefold is related to the integrations of various Chern-Weil forms. We proved that all these integrals are finite (and also rational).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-17T23:47:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moduli space",
      "gauss-bonnet-chern theorem",
      "chern-weil forms",
      "weil-petersson metric",
      "polarized kahler manifolds"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 815940,
      "adsabs": "2009arXiv0902.3839L"
    }
  }
}