{
  "id": "1606.07706",
  "version": "v1",
  "published": "2016-06-24T14:42:09.000Z",
  "updated": "2016-06-24T14:42:09.000Z",
  "title": "Geometry and Topology of the space of Kähler metrics on singular varieties",
  "authors": [
    "Eleonora Di Nezza",
    "Vincent Guedj"
  ],
  "comment": "45 pages. arXiv admin note: substantial text overlap with arXiv:1401.7857",
  "categories": [
    "math.DG",
    "math.CV"
  ],
  "abstract": "Let $Y$ be a compact K\\\"ahler normal space and $\\alpha \\in H^{1,1}(Y,\\mathbb{R})$ a K\\\"ahler class. We study metric properties of the space $\\mathcal{H}_\\alpha$ of K\\\"ahler metrics in $\\alpha$ using Mabuchi geodesics. We extend several results by Calabi, Chen, Darvas previously established when the underlying space is smooth. As an application we analytically characterize the existence of K\\\"ahler-Einstein metrics on $\\mathbb{Q}$-Fano varieties, generalizing a result of Tian, and illustrate these concepts in the case of toric varieties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-24T14:42:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kähler metrics",
      "singular varieties",
      "study metric properties",
      "normal space",
      "mabuchi geodesics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}