{
  "id": "math/0703344",
  "version": "v4",
  "published": "2007-03-12T14:56:09.000Z",
  "updated": "2008-01-21T21:26:43.000Z",
  "title": "Bergman kernels and the pseudoeffectivity of relative canonical bundles",
  "authors": [
    "Bo Berndtsson",
    "Mihai Paun"
  ],
  "comment": "This is the third revision",
  "journal": "Duke Math J 145 (2008), no 2 pp 341-378",
  "categories": [
    "math.AG",
    "math.CV"
  ],
  "abstract": "The main result of the present article is a (practically optimal) criterium for the pseudoeffectivity of the twisted relative canonical bundles of surjective projective maps. Our theorem has several applications in algebraic geometry; to start with, we obtain the natural analytic generalization of some semipositivity results due to E. Viehweg and F. Campana. As a byproduct, we give a simple and direct proof of a recent result due to C. Hacon--J. McKernan, S. Takayama and H. Tsuji concerning the extension of twisted pluricanonical forms. More applications will be offered in the sequel of this article.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2008-01-21T21:26:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D06"
    ],
    "keywords": [
      "relative canonical bundles",
      "bergman kernels",
      "pseudoeffectivity",
      "natural analytic generalization",
      "applications"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3344B"
    }
  }
}