{
  "id": "1012.0109",
  "version": "v2",
  "published": "2010-12-01T06:44:42.000Z",
  "updated": "2010-12-18T12:01:42.000Z",
  "title": "New Constructions of Complex Manifolds",
  "authors": [
    "Jinxing Xu"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AG",
    "math.DG"
  ],
  "abstract": "For a generic anti-canonical hypersurface in each smooth toric Fano 4-fold with rank 2 Picard group, we prove there exist three isolated rational curves in it. Moreover, for all these 4-folds except one, the contractions of generic anti-canonical hypersurfaces along the three rational curves can be deformed to smooth threefolds diffeomorphic to connected sums of S^{3} \\times S^{3}. In this manner, we obtain complex structures with trivial canonical bundles on some connected sums of S^{3} \\times S^{3}. This construction is an analogue of that in Friedman [7], Lu and Tian [12] which used only quintics in P^{4}.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-12-18T12:01:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex manifolds",
      "generic anti-canonical hypersurface",
      "construction",
      "smooth toric fano",
      "connected sums"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.0109X"
    }
  }
}