{
  "id": "0809.1787",
  "version": "v1",
  "published": "2008-09-10T13:29:04.000Z",
  "updated": "2008-09-10T13:29:04.000Z",
  "title": "3-Dimensional Lattice Polytopes Without Interior Lattice Points",
  "authors": [
    "Jaron Treutlein"
  ],
  "comment": "12 pages, 3 figures",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "A theorem of Howe states that every 3-dimensional lattice polytope $P$ whose only lattice points are its vertices, is a Cayley polytope, i.e. $P$ is the convex hull of two lattice polygons with distance one. We want to generalize this result by classifying 3-dimensional lattice polytopes without interior lattice points. The main result will be, that they are up to finite many exceptions either Cayley polytopes or there is a projection, which maps the polytope to the double unimodular 2-simplex. To every such polytope we associate a smooth projective surface of genus 0.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-10T13:29:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B20",
      "14M25"
    ],
    "keywords": [
      "interior lattice points",
      "lattice polytope",
      "cayley polytope",
      "lattice polygons",
      "smooth projective surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.1787T"
    }
  }
}