{
  "id": "0710.5724",
  "version": "v1",
  "published": "2007-10-30T19:34:07.000Z",
  "updated": "2007-10-30T19:34:07.000Z",
  "title": "Existence of Kähler-Einstein metrics and multiplier ideal sheaves on del Pezzo surfaces",
  "authors": [
    "Gordon Heier"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AG",
    "math.CV",
    "math.DG"
  ],
  "abstract": "We apply Nadel's method of multiplier ideal sheaves to show that every complex del Pezzo surface of degree at most six whose automorphism group acts without fixed points has a K\\\"ahler-Einstein metric. In particular, all del Pezzo surfaces of degree $4,5$, or $6$ and certain special del Pezzo surfaces of lower degree are shown to have a K\\\"ahler-Einstein metric. This result is not new, but the proofs given in the present paper are less involved than earlier ones by Siu, Tian and Tian-Yau.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-10-30T19:34:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J26",
      "14J45",
      "32Q20"
    ],
    "keywords": [
      "multiplier ideal sheaves",
      "kähler-einstein metrics",
      "special del pezzo surfaces",
      "complex del pezzo surface",
      "automorphism group acts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.5724H"
    }
  }
}