{
  "id": "1111.3236",
  "version": "v2",
  "published": "2011-11-14T14:59:03.000Z",
  "updated": "2012-01-19T01:43:51.000Z",
  "title": "The augmented base locus in positive characteristic",
  "authors": [
    "Paolo Cascini",
    "James McKernan",
    "Mircea Mustata"
  ],
  "comment": "9 pages; v.2: minor corrections, to appear in Proceedings of the Edinburgh Mathematical Society, volume dedicated to V.V. Shokurov",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let L be a nef line bundle on a projective scheme X in positive characteristic. We prove that the augmented base locus of L is equal to the union of the irreducible closed subsets V of X such that the restriction of L to V is not big. For a smooth variety in characteristic zero, this was proved by Nakamaye using vanishing theorems.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-19T01:43:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14A15",
      "14E99"
    ],
    "keywords": [
      "augmented base locus",
      "positive characteristic",
      "nef line bundle",
      "smooth variety",
      "characteristic zero"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.3236C"
    }
  }
}