{
  "id": "1401.0510",
  "version": "v3",
  "published": "2014-01-02T19:21:38.000Z",
  "updated": "2015-12-18T20:56:48.000Z",
  "title": "The second Betti number of hyperkähler manifolds",
  "authors": [
    "Nikon Kurnosov"
  ],
  "comment": "7 pages. Major changes",
  "categories": [
    "math.AG",
    "math.DG"
  ],
  "abstract": "Let $M$ be a compact irreducible hyperkahler manifold, from Bogomolov inequality [V1] we obtain forbidden values of the second Betti number $b_2$ in arbitrary dimension. UPD: Unfortunately, decomposition of dual to BBF-form is not right in the main theorem. Instead of this work, take a look on recent preprints of Sawon and me on boundedness of $b_2$ for hyperk\\\"ahler manifolds.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-01-07T20:33:15.000Z",
      "abstract": "Let $M$ be a compact irreducible hyperkahler manifold, from Bogomolov inequality [V1] we obtain forbidden values of the second Betti number $b_2$ in arbitrary dimension.",
      "comment": "7 pages. Minor changes",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-12-18T20:56:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14K22",
      "53C26"
    ],
    "keywords": [
      "second betti number",
      "hyperkähler manifolds",
      "compact irreducible hyperkahler manifold",
      "bogomolov inequality",
      "forbidden values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.0510K"
    }
  }
}