{
  "id": "0902.0861",
  "version": "v1",
  "published": "2009-02-05T08:28:28.000Z",
  "updated": "2009-02-05T08:28:28.000Z",
  "title": "On the existence of Kähler metrics of constant scalar curvature",
  "authors": [
    "Kenji Tsuboi"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "For certain compact complex Fano manifolds $M$ with reductive Lie algebras of holomorphic vector fields, we determine the analytic subvariety of the second cohomology group of $M$ consisting of K\\\"ahler classes whose Bando-Calabi-Futaki character vanishes. Then a K\\\"ahler class contains a K\\\"ahler metric of constant scalar curvature if and only if the K\\\"ahler class is contained in the analytic subvariety. On examination of the analytic subvariety, it is shown that $M$ admits infinitely many nonhomothetic K\\\"ahler classes containing K\\\"ahler metrics of constant scalar curvature but does not admit any K\\\"ahler-Einstein metric.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-05T08:28:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C25",
      "53C55"
    ],
    "keywords": [
      "constant scalar curvature",
      "kähler metrics",
      "analytic subvariety",
      "compact complex fano manifolds",
      "bando-calabi-futaki character vanishes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.0861T"
    }
  }
}