{
  "id": "0905.4718",
  "version": "v2",
  "published": "2009-05-28T19:24:12.000Z",
  "updated": "2009-10-23T21:55:10.000Z",
  "title": "Adiabatic limits of Ricci-flat Kahler metrics",
  "authors": [
    "Valentino Tosatti"
  ],
  "comment": "26 pages; final version to appear in J. Differential Geom",
  "journal": "J. Differential Geom. 84 (2010), no.2, 427-453",
  "categories": [
    "math.DG"
  ],
  "abstract": "We study adiabatic limits of Ricci-flat Kahler metrics on a Calabi-Yau manifold which is the total space of a holomorphic fibration when the volume of the fibers goes to zero. By establishing some new a priori estimates for the relevant complex Monge-Ampere equation, we show that the Ricci-flat metrics collapse (away from the singular fibers) to a metric on the base of the fibration. This metric has Ricci curvature equal to a Weil-Petersson metric that measures the variation of complex structure of the Calabi-Yau fibers. This generalizes results of Gross-Wilson for K3 surfaces to higher dimensions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-10-23T21:55:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32Q25",
      "14J32",
      "32Q20",
      "53C25"
    ],
    "keywords": [
      "ricci-flat kahler metrics",
      "relevant complex monge-ampere equation",
      "study adiabatic limits",
      "ricci-flat metrics collapse",
      "ricci curvature equal"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.4718T"
    }
  }
}