{
  "id": "1010.3887",
  "version": "v2",
  "published": "2010-10-19T12:52:38.000Z",
  "updated": "2013-07-17T13:41:11.000Z",
  "title": "Few smooth d-polytopes with n lattice points",
  "authors": [
    "Tristram Bogart",
    "Christian Haase",
    "Milena Hering",
    "Benjamin Lorenz",
    "Benjamin Nill",
    "Andreas Paffenholz",
    "Günter Rote",
    "Francisco Santos",
    "Hal Schenck"
  ],
  "comment": "20+2 pages; major revision: new author, new structure, new results",
  "categories": [
    "math.AG",
    "math.CO",
    "math.SG"
  ],
  "abstract": "We prove that, for fixed n there exist only finitely many embeddings of Q-factorial toric varieties X into P^n that are induced by a complete linear system. The proof is based on a combinatorial result that for fixed nonnegative integers d and n, there are only finitely many smooth d-polytopes with n lattice points. We also enumerate all smooth 3-polytopes with at most 12 lattice points. In fact, it is sufficient to bound the singularities and the number of lattice points on edges to prove finiteness.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-07-17T13:41:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M25",
      "52B20"
    ],
    "keywords": [
      "lattice points",
      "smooth d-polytopes",
      "q-factorial toric varieties",
      "complete linear system",
      "combinatorial result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 2,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.3887B"
    }
  }
}