{
  "id": "math/0201031",
  "version": "v1",
  "published": "2002-01-05T11:41:32.000Z",
  "updated": "2002-01-05T11:41:32.000Z",
  "title": "On the volume of a line bundle",
  "authors": [
    "Sebastien Boucksom"
  ],
  "categories": [
    "math.AG",
    "math.CV"
  ],
  "abstract": "Using a result of Fujita on approximate Zariski decompositions and the singular version of Demailly's holomorphic Morse inequalities as obtained by Bonavero, we express the volume of a line bundle in terms of the absolutely continuous parts of all the positive curvature currents on it, with a way to pick an element among them which is most homogeneous with respect to the volume. This enables us to introduce the volume of any pseudoeffective class on a compact Kaehler manifold, and Fujita's theorem is then extended to this context.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-01-05T11:41:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32J25",
      "32J27",
      "14C20"
    ],
    "keywords": [
      "line bundle",
      "demaillys holomorphic morse inequalities",
      "approximate zariski decompositions",
      "compact kaehler manifold",
      "fujitas theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......1031B"
    }
  }
}