{
  "id": "hep-th/9507075",
  "version": "v1",
  "published": "1995-07-13T10:19:06.000Z",
  "updated": "1995-07-13T10:19:06.000Z",
  "title": "Dual Polyhedra, Mirror Symmetry and Landau-Ginzburg Orbifolds",
  "authors": [
    "Hitoshi Sato"
  ],
  "comment": "8 pages, Latex",
  "journal": "Mod.Phys.Lett. A11 (1996) 389-396",
  "doi": "10.1142/S0217732396000436",
  "categories": [
    "hep-th",
    "alg-geom",
    "math.AG"
  ],
  "abstract": "New geometrical features of the Landau-Ginzburg orbifolds are presented, for models with a typical type of superpotential. We show the one-to-one correspondence between some of the $(a,c)$ states with $U(1)$ charges $(-1,1)$ and the integral points on the dual polyhedra, which are useful tools for the construction of mirror manifolds. Relying on toric geometry, these states are shown to correspond to the $(1,1)$ forms coming from blowing-up processes. In terms of the above identification, it can be checked that the monomial-divisor mirror map for Landau-Ginzburg orbifolds, proposed by the author, is equivalent to that mirror map for Calabi-Yau manifolds obtained by the mathematicians.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1995-07-13T10:19:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "landau-ginzburg orbifolds",
      "dual polyhedra",
      "mirror symmetry",
      "monomial-divisor mirror map",
      "one-to-one correspondence"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 397253
    }
  }
}