{
  "id": "1704.07812",
  "version": "v1",
  "published": "2017-04-25T17:42:01.000Z",
  "updated": "2017-04-25T17:42:01.000Z",
  "title": "Discrete Symmetries of Calabi-Yau Hypersurfaces in Toric Four-Folds",
  "authors": [
    "Andreas Braun",
    "Andre Lukas",
    "Chuang Sun"
  ],
  "categories": [
    "hep-th",
    "math.AG"
  ],
  "abstract": "We analyze freely-acting discrete symmetries of Calabi-Yau three-folds defined as hypersurfaces in ambient toric four-folds. An algorithm which allows the systematic classification of such symmetries which are linearly realised on the toric ambient space is devised. This algorithm is applied to all Calabi-Yau manifolds with $h^{1,1}(X)\\leq 3$ obtained by triangulation from the Kreuzer-Skarke list, a list of some $350$ manifolds. All previously known freely-acting symmetries on these manifolds are correctly reproduced and we find five manifolds with freely-acting symmetries. These include a single new example, a manifold with a $\\mathbb{Z}_2\\times\\mathbb{Z}_2$ symmetry where only one of the $\\mathbb{Z}_2$ factors was previously known. In addition, a new freely-acting $\\mathbb{Z}_2$ symmetry is constructed for a manifold with $h^{1,1}(X)=6$. While our results show that there are more freely-acting symmetries within the Kreuzer-Skarke set than previously known, it appears that such symmetries are relatively rare.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-25T17:42:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "calabi-yau hypersurfaces",
      "freely-acting symmetries",
      "analyze freely-acting discrete symmetries",
      "toric ambient space",
      "ambient toric four-folds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}