{
  "id": "math/0312032",
  "version": "v1",
  "published": "2003-12-01T16:43:57.000Z",
  "updated": "2003-12-01T16:43:57.000Z",
  "title": "On the homotopy types of compact kaehler and complex projective manifolds",
  "authors": [
    "Claire Voisin"
  ],
  "comment": "To appear in Inventiones Math",
  "categories": [
    "math.AG",
    "math.SG"
  ],
  "abstract": "We show that in every dimension greater than or equal to 4, there exist compact Kaehler manifolds which do not have the homotopy type of projective complex manifolds. Thus they a fortiori are not deformation equivalent to a projective manifold, which solves negatively Kodaira's problem. We give both non simply connected (of dimension at least 4) and simply connected (of dimension at least 6) such examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-12-01T16:43:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex projective manifolds",
      "homotopy type",
      "compact kaehler manifolds",
      "projective complex manifolds",
      "deformation equivalent"
    ],
    "publication": {
      "doi": "10.1007/s00222-003-0352-1",
      "journal": "Inventiones Mathematicae",
      "year": 2004,
      "month": "Aug",
      "volume": 157,
      "number": 2,
      "pages": 329
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004InMat.157..329V"
    }
  }
}