{
  "id": "0907.1387",
  "version": "v2",
  "published": "2009-07-09T07:43:49.000Z",
  "updated": "2012-07-09T02:18:56.000Z",
  "title": "Numerical Weil-Petersson metrics on moduli spaces of Calabi-Yau manifolds",
  "authors": [
    "Julien Keller",
    "Sergio Lukic"
  ],
  "comment": "28 pages, 8 figures",
  "categories": [
    "math.DG",
    "hep-th"
  ],
  "abstract": "We introduce a simple and very fast algorithm that computes Weil-Petersson metrics on moduli spaces of polarized Calabi-Yau manifolds. Also, by using Donaldson's quantization link between the infinite and finite dimensional G.I.T quotients that describe moduli spaces of varieties, we define a natural sequence of Kaehler metrics. We prove that the sequence converges to the Weil-Petersson metric. We also develop an algorithm that numerically approximates such metrics, and hence the Weil-Petersson metric itself. Explicit examples are provided on a family of Calabi-Yau Quintic hypersurfaces in CP^4. The scope of our second algorithm is much broader; the same techniques can be used to approximate metrics on null spaces of Dirac operators coupled to Hermite Yang-Mills connections.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-07-09T02:18:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moduli spaces",
      "numerical weil-petersson metrics",
      "calabi-yau manifolds",
      "hermite yang-mills connections",
      "donaldsons quantization link"
    ],
    "publication": {
      "doi": "10.1016/j.geomphys.2015.02.018"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 825342,
      "adsabs": "2009arXiv0907.1387K"
    }
  }
}