{
  "id": "1310.0774",
  "version": "v5",
  "published": "2013-10-02T17:18:47.000Z",
  "updated": "2015-05-29T11:08:32.000Z",
  "title": "Tonoli's Calabi--Yau threefolds revisited",
  "authors": [
    "Grzegorz Kapustka",
    "Michal Kapustka"
  ],
  "comment": "title changed, paper reorganized; 18 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We find a simple geometric construction of Tonoli's examples of Calabi--Yau threefolds of degree 17 in complex $\\mathbb{P}^6$. We prove that the rank of the Picard group of elements of one of these families is at least $2$.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-06-24T19:46:09.000Z",
      "title": "Del Pezzo surfaces in $\\mathbb{P}^5$ and Calabi--Yau threefolds in $\\mathbb{P}^6$",
      "abstract": "We find a simple geometric construction of Tonoli examples of Calabi--Yau threefolds of degree 17 in complex $\\mathbb{P}^6$. We then observe and investigate an analogy between the descriptions in terms of Pfaffians of vector bundles of anti-canonically embedded del Pezzo surfaces in $\\mathbb{P}^5$ and of known Calabi--Yau threefolds in $\\mathbb{P}^6$.",
      "comment": "minor changes",
      "journal": null,
      "doi": null
    },
    {
      "version": "v5",
      "updated": "2015-05-29T11:08:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J32"
    ],
    "keywords": [
      "calabi-yau threefolds",
      "anti-canonically embedded del pezzo surfaces",
      "simple geometric construction",
      "vector bundles",
      "tonoli examples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.0774K"
    }
  }
}