{
  "id": "1206.6521",
  "version": "v3",
  "published": "2012-06-27T20:49:04.000Z",
  "updated": "2013-06-12T03:34:24.000Z",
  "title": "On the numerical dimension of pseudo-effective divisors in positive characteristic",
  "authors": [
    "Paolo Cascini",
    "Christopher Hacon",
    "Mircea Mustata",
    "Karl Schwede"
  ],
  "comment": "v.3 (17 pages): typos corrected and other minor changes. Additional remarks on the singular case. To appear in the American Journal of Mathematics",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let X be a smooth projective variety over an algebraically closed field of positive characteristic. We prove that if D is a pseudo-effective R-divisor on X which is not numerically equivalent to the negative part in its divisorial Zariski decomposition, then the numerical dimension of D is positive. In characteristic zero, this was proved by Nakayama using vanishing theorems.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-06-12T03:34:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E99",
      "13A35",
      "14F18"
    ],
    "keywords": [
      "positive characteristic",
      "numerical dimension",
      "pseudo-effective divisors",
      "divisorial zariski decomposition",
      "smooth projective variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.6521C"
    }
  }
}