{
  "id": "1511.08778",
  "version": "v1",
  "published": "2015-11-27T19:54:46.000Z",
  "updated": "2015-11-27T19:54:46.000Z",
  "title": "Calabi-Yau threefolds of type K (II): Mirror symmetry",
  "authors": [
    "Kenji Hashimoto",
    "Atsushi Kanazawa"
  ],
  "comment": "24 pages, comments welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "A Calabi-Yau threefold is called of type K if it admits an \\'etale Galois covering by the product of a K3 surface and an elliptic curve. In our previous paper, based on Oguiso-Sakurai's fundamental work, we provide the full classification of Calabi-Yau threefolds of type K and study some basic properties thereof. In the present paper, we continue the study, investigating them from the viewpoint of mirror symmetry. It is shown that mirror symmetry relies on a duality of certain sublattices in the second cohomology of the K3 surface appearing in the minimal splitting covering. The duality may be thought of as a version of the lattice duality of the anti-symplectic involution on K3 surfaces discovered by Nikulin. Based on the duality, we obtain several results parallel to what is known for Borcea-Voisin threefolds. Along the way, we also investigate the Brauer groups of Calabi-Yau threefolds of type K.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-27T19:54:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J32",
      "14J28",
      "14F45"
    ],
    "keywords": [
      "calabi-yau threefold",
      "k3 surface",
      "basic properties thereof",
      "oguiso-sakurais fundamental work",
      "mirror symmetry relies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1407250
    }
  }
}