{
  "id": "1209.3186",
  "version": "v3",
  "published": "2012-09-14T13:35:37.000Z",
  "updated": "2014-06-13T09:19:49.000Z",
  "title": "Smooth Fano Polytopes With Many Vertices",
  "authors": [
    "Benjamin Assarf",
    "Michael Joswig",
    "Andreas Paffenholz"
  ],
  "comment": "34 pages, to appear in Discrete & Computational Geometry",
  "categories": [
    "math.AG",
    "math.CO"
  ],
  "abstract": "We classify the d-dimensional simplicial, terminal, and reflexive polytopes with at least 3d-2 vertices. In particular, it turns out that these are all smooth Fano polytopes. This improves on previous results of Casagrande in 2006 and Oebro in 2008. Smooth Fano polytopes play a role in algebraic geometry and mathematical physics.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-06-13T09:19:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B20",
      "14M25",
      "14J45"
    ],
    "keywords": [
      "smooth fano polytopes play",
      "algebraic geometry",
      "d-dimensional simplicial",
      "casagrande",
      "reflexive polytopes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}