{
  "id": "math/0703456",
  "version": "v2",
  "published": "2007-03-15T15:20:39.000Z",
  "updated": "2007-04-26T13:59:20.000Z",
  "title": "Combinatorial aspects of mirror symmetry",
  "authors": [
    "Victor Batyrev",
    "Benjamin Nill"
  ],
  "comment": "AMS-LaTeX, 37 pages, 3 figures; conjecture 4.10 refined, bibliography updated",
  "journal": "Contemporary Mathematics 452 (2008), 35-66",
  "categories": [
    "math.CO",
    "hep-th",
    "math.AG"
  ],
  "abstract": "The purpose of this paper is to review some combinatorial ideas behind the mirror symmetry for Calabi-Yau hypersurfaces and complete intersections in Gorenstein toric Fano varieties. We suggest as a basic combinatorial object the notion of a Gorenstein polytope of index r. A natural combinatorial duality for d-dimensional Gorenstein polytopes of index r extends the well-known polar duality for reflexive polytopes (case r=1). We consider the Borisov duality between two nef-partitions as a duality between two Gorenstein polytopes P and P^* of index r together with selected special (r-1)-dimensional simplices S in P and S' in P^*. Different choices of these simplices suggest an interesting relation to Homological Mirror Symmetry.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-04-26T13:59:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B20",
      "14M25",
      "14J32"
    ],
    "keywords": [
      "combinatorial aspects",
      "gorenstein toric fano varieties",
      "natural combinatorial duality",
      "d-dimensional gorenstein polytopes",
      "basic combinatorial object"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 749018,
      "adsabs": "2007math......3456B"
    }
  }
}