{
  "id": "1103.2202",
  "version": "v4",
  "published": "2011-03-11T06:51:18.000Z",
  "updated": "2014-06-30T07:10:28.000Z",
  "title": "Smooth Fano polytopes arising from finite directed graphs",
  "authors": [
    "Akihiro Higashitani"
  ],
  "comment": "13 pages, 4 figures",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "In this paper, we consider terminal reflexive polytopes arising from finite directed graphs and study the problem of deciding which directed graphs yield smooth Fano polytopes. We show that any centrally symmetric or pseudo-symmetric smooth Fano polytopes can be obtained from directed graphs. Moreover, by using directed graphs, we provide new examples of smooth Fano polytopes whose corresponding varieties admit K\\\"ahler--Einstein metrics.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-06-30T07:10:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M25",
      "52B20",
      "05C20"
    ],
    "keywords": [
      "smooth fano polytopes arising",
      "finite directed graphs",
      "graphs yield smooth fano polytopes",
      "pseudo-symmetric smooth fano polytopes",
      "directed graphs yield smooth fano"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.2202H"
    }
  }
}