{
  "id": "math/0003230",
  "version": "v1",
  "published": "2000-03-31T13:43:23.000Z",
  "updated": "2000-03-31T13:43:23.000Z",
  "title": "Characterizations of ${\\mathbb P}^n$ in arbitrary characteristic",
  "authors": [
    "Yasuyuki Kachi",
    "János Kollár"
  ],
  "comment": "10 pages, LaTeX",
  "categories": [
    "math.AG"
  ],
  "abstract": "We prove that a smooth projective variety of dimension n is isomorphic to projective n-space iff the canonical class is -(n+1)-times an ample divisor. In characteristic zero this was proved by Kobayashi-Ochiai. We also extend the second adjunction theorem of Ionescu and Fujita to arbitrary characteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-03-31T13:43:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C20",
      "14J40",
      "14J45"
    ],
    "keywords": [
      "arbitrary characteristic",
      "characterizations",
      "second adjunction theorem",
      "smooth projective variety",
      "ample divisor"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......3230K"
    }
  }
}