{
  "id": "math/0505432",
  "version": "v1",
  "published": "2005-05-20T14:37:49.000Z",
  "updated": "2005-05-20T14:37:49.000Z",
  "title": "Integral Cohomology and Mirror Symmetry for Calabi-Yau 3-folds",
  "authors": [
    "Victor Batyrev",
    "Maximilian Kreuzer"
  ],
  "comment": "18 pages, AMS-LaTeX",
  "categories": [
    "math.AG",
    "hep-th",
    "math.AT"
  ],
  "abstract": "In this paper, we compute the integral cohomology groups for all examples of Calabi-Yau 3-folds obtained from hypersurfaces in 4-dimensional Gorenstein toric Fano varieties. Among 473 800 776 families of Calabi-Yau 3-folds $X$ corresponding to 4-dimensional reflexive polytopes there exist exactly 32 families having non-trivial torsion in $H^*(X, \\Z)$. We came to an interesting observation that the torsion subgroups in $H^2$ and $H^3$ are exchanged by the mirror symmetry involution, i.e. the torsion subgroup in the Picard group of $X$ is isomorphic to the Brauer group of the mirror $X^*$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-05-20T14:37:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J32",
      "14M25"
    ],
    "keywords": [
      "calabi-yau",
      "torsion subgroup",
      "gorenstein toric fano varieties",
      "mirror symmetry involution",
      "integral cohomology groups"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 683209,
      "adsabs": "2005math......5432B"
    }
  }
}