{
  "id": "math/0602336",
  "version": "v3",
  "published": "2006-02-15T17:57:58.000Z",
  "updated": "2006-06-01T10:19:24.000Z",
  "title": "Multiples of lattice polytopes without interior lattice points",
  "authors": [
    "Victor Batyrev",
    "Benjamin Nill"
  ],
  "comment": "AMS-LaTeX, 13 pages; typos corrected, reference added",
  "journal": "Moscow Math. J. 7 (2007), 195-207",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "Let $\\Delta$ be an $n$-dimensional lattice polytope. The smallest non-negative integer $i$ such that $k \\Delta$ contains no interior lattice points for $1 \\leq k \\leq n - i$ we call the degree of $\\Delta$. We consider lattice polytopes of fixed degree $d$ and arbitrary dimension $n$. Our main result is a complete classification of $n$-dimensional lattice polytopes of degree $d=1$. This is a generalization of the classification of lattice polygons $(n=2)$ without interior lattice points due to Arkinstall, Khovanskii, Koelman and Schicho. Our classification shows that the secondary polytope of a lattice polytope of degree 1 is always a simple polytope.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-06-01T10:19:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B20",
      "14M25"
    ],
    "keywords": [
      "interior lattice points",
      "dimensional lattice polytope",
      "smallest non-negative integer",
      "lattice polygons",
      "simple polytope"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......2336B"
    }
  }
}