{
  "id": "math/0703810",
  "version": "v3",
  "published": "2007-03-27T15:18:20.000Z",
  "updated": "2008-01-24T10:36:54.000Z",
  "title": "Primitive contractions of Calabi-Yau threefolds I",
  "authors": [
    "Grzegorz Kapustka",
    "Michal Kapustka"
  ],
  "comment": "23 pages, the numeration of subarticles changed",
  "categories": [
    "math.AG"
  ],
  "abstract": "We construct examples of primitive contractions of Calabi--Yau threefolds with exceptional locus being $ \\mathbb{P}^1 \\times \\mathbb{P}^1$, $\\mathbb{P}^2$, and smooth del Pezzo surfaces of degrees $\\leq 5$. We describe the images of these primitive contractions and find their smoothing families. In particular, we give a method to compute the Hodge numbers of a generic fiber of the smoothing family of each Calabi--Yau threefold with one isolated singularity obtained after a primitive contraction of type II. As an application, we get examples of natural conifold transitions between some families of Calabi--Yau threefolds.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-01-24T10:36:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J32",
      "14J10"
    ],
    "keywords": [
      "calabi-yau threefold",
      "primitive contraction",
      "smooth del pezzo surfaces",
      "natural conifold transitions",
      "hodge numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3810K"
    }
  }
}