{
  "id": "1206.4827",
  "version": "v1",
  "published": "2012-06-21T10:35:17.000Z",
  "updated": "2012-06-21T10:35:17.000Z",
  "title": "A classification of smooth convex 3-polytopes with at most 16 lattice points",
  "authors": [
    "Anders Lundman"
  ],
  "comment": "25 pages, 130 figures; Journal of Algebraic Combinatorics Online First, 2012",
  "doi": "10.1007/s10801-012-0363-3",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "We provide a complete classification up to isomorphism of all smooth convex lattice 3-polytopes with at most 16 lattice points. There exist in total 103 different polytopes meeting these criteria. Of these, 99 are strict Cayley polytopes and the remaining 4 are obtained as inverse stellar subdivisions of such polytopes. We derive a classification, up to isomorphism, of all smooth embeddings of toric threefolds in $\\mathbb{P}^N$ where $N\\le 15$. Again we have in total 103 such embeddings. Of these, 99 are projective bundles embedded in $\\mathbb{P}^N$ and the remaining 4 are blow-ups of such toric threefolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-21T10:35:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lattice points",
      "toric threefolds",
      "inverse stellar subdivisions",
      "strict cayley polytopes",
      "smooth convex lattice"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.4827L"
    }
  }
}