{
  "id": "1412.1426",
  "version": "v1",
  "published": "2014-12-03T18:28:57.000Z",
  "updated": "2014-12-03T18:28:57.000Z",
  "title": "Alpha invariants and coercivity of the Mabuchi functional on Fano manifolds",
  "authors": [
    "Ruadhaí Dervan"
  ],
  "comment": "13 pages, comments welcome",
  "categories": [
    "math.DG",
    "math.CV"
  ],
  "abstract": "We give a criterion for the coercivity of the Mabuchi functional for general K\\\"ahler classes on Fano manifolds in terms of Tian's alpha invariant. This generalises a result of Tian in the anti-canonical case implying the existence of a K\\\"ahler-Einstein metric. As an application, we provide new K\\\"ahler classes on a general degree one del Pezzo surface for which the Mabuchi functional is coercive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-03T18:28:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mabuchi functional",
      "fano manifolds",
      "coercivity",
      "tians alpha invariant",
      "del pezzo surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.1426D"
    }
  }
}