{
  "id": "0804.1682",
  "version": "v1",
  "published": "2008-04-10T12:07:03.000Z",
  "updated": "2008-04-10T12:07:03.000Z",
  "title": "Non-algebraic Hyperkaehler manifolds",
  "authors": [
    "Frederic Campana",
    "Keiji Oguiso",
    "Thomas Peternell"
  ],
  "comment": "18 pages",
  "categories": [
    "math.DG",
    "math.AG"
  ],
  "abstract": "We study the algebraic dimension a(X) of a compact hyperkaehler manfold of dimension 2n. We show that a(X) is at most n unless X is projective. If a compact Kaehler manifold with algebraic dimension 0 and Kodaira dimension 0 has a minimal model, then only the values 0,n and 2n are possible. In case of middle dimension, the algebraic reduction is holomorphic Lagrangian. If n = 2, then - without any assumptions - the algebraic dimension only takes the values 0,2 and 4. The paper gives structure results for \"generalised hyperkaehler\" manifolds and studies nef lines bundles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-10T12:07:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32J27",
      "14J99"
    ],
    "keywords": [
      "non-algebraic hyperkaehler manifolds",
      "algebraic dimension",
      "studies nef lines bundles",
      "compact hyperkaehler manfold",
      "compact kaehler manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.1682C"
    }
  }
}