{
  "id": "math/0104172",
  "version": "v1",
  "published": "2001-04-17T18:46:18.000Z",
  "updated": "2001-04-17T18:46:18.000Z",
  "title": "Hyperplane sections of Calabi-Yau varieties",
  "authors": [
    "Jonathan Wahl"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Theorem: If W is a smooth complex projective variety with h^1 (O-script_W) = 0, then a sufficiently ample smooth divisor X on W cannot be a hyperplane section of a Calabi-Yau variety, unless W is itself a Calabi-Yau. Corollary: A smooth hypersurface of degree d in P^n (n >= 2) is a hyperplane section of a Calabi-Yau variety iff n+2 <= d <= 2n+2. The method is to construct out of the variety W a universal family of all varieties Z for which X is a hyperplane section with normal bundle K_X, and examine the \"bad\" singularities of such Z. A motivation is to show many curves cannot be divisors on a K-3 surface.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-04-17T18:46:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J32",
      "14D15"
    ],
    "keywords": [
      "hyperplane section",
      "calabi-yau variety",
      "smooth complex projective variety",
      "sufficiently ample smooth divisor",
      "smooth hypersurface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......4172W"
    }
  }
}