{
  "id": "1004.3446",
  "version": "v1",
  "published": "2010-04-20T13:37:08.000Z",
  "updated": "2010-04-20T13:37:08.000Z",
  "title": "Representations on the cohomology of hypersurfaces and mirror symmetry",
  "authors": [
    "Alan Stapledon"
  ],
  "comment": "34 pages",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "We study the representation of a finite group acting on the cohomology of a non-degenerate, invariant hypersurface of a projective toric variety. We deduce an explicit description of the representation when the toric variety has at worst quotient singularities. As an application, we conjecture a representation-theoretic version of Batyrev and Borisov's mirror symmetry between pairs of Calabi-Yau hypersurfaces, and prove it when the hypersurfaces are both smooth or have dimension at most 3. An interesting consequence is the existence of pairs of Calabi-Yau orbifolds whose Hodge diamonds are mirror, with respect to the usual Hodge structure on singular cohomology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-20T13:37:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L30",
      "14M25"
    ],
    "keywords": [
      "representation",
      "usual hodge structure",
      "borisovs mirror symmetry",
      "worst quotient singularities",
      "calabi-yau orbifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.3446S"
    }
  }
}