{
  "id": "1211.2058",
  "version": "v2",
  "published": "2012-11-09T07:19:04.000Z",
  "updated": "2013-05-06T13:01:00.000Z",
  "title": "Deformation of Kähler manifolds",
  "authors": [
    "Junyan Cao"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "It has been shown by Claire Voisin in 2003 that one cannot always deform a compact K\\\"ahler manifold into a projective algebraic manifold, thereby answering negatively a question raised by Kodaira. In this article, we prove that under an additional semipositivity or seminegativity condition on the canonical bundle, the answer becomes positive, namely such a compact K\\\"ahler manifold can be approximated by deformations of projective manifolds.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-06T13:01:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kähler manifolds",
      "deformation",
      "claire voisin",
      "additional semipositivity",
      "seminegativity condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.2058C"
    }
  }
}