{
  "id": "math/0412480",
  "version": "v3",
  "published": "2004-12-23T15:04:28.000Z",
  "updated": "2007-01-15T16:10:33.000Z",
  "title": "Volume and lattice points of reflexive simplices",
  "authors": [
    "Benjamin Nill"
  ],
  "comment": "AMS-LaTeX, 19 pages; paper reorganized, introduction added, bibliography updated; typos corrected",
  "journal": "Discr. Comp. Geom. 37 (2007), 301-320",
  "doi": "10.1007/s00454-006-1299-y",
  "categories": [
    "math.AG",
    "math.CO",
    "math.NT"
  ],
  "abstract": "We prove sharp upper bounds on the volume and the number of lattice points on edges of higher-dimensional reflexive simplices. These convex-geometric results are derived from new number-theoretic bounds on the denominators of unit fractions summing up to one. The main algebro-geometric application is a sharp upper bound on the anticanonical degree of higher-dimensional Q-factorial Gorenstein toric Fano varieties with Picard number one, where we completely characterize the case of equality.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-01-15T16:10:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M25",
      "14J45",
      "52B20",
      "11D75",
      "11H06"
    ],
    "keywords": [
      "lattice points",
      "reflexive simplices",
      "sharp upper bound",
      "higher-dimensional q-factorial gorenstein toric fano",
      "q-factorial gorenstein toric fano varieties"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....12480N"
    }
  }
}