{
  "id": "0804.3667",
  "version": "v1",
  "published": "2008-04-23T09:15:11.000Z",
  "updated": "2008-04-23T09:15:11.000Z",
  "title": "Cayley decompositions of lattice polytopes and upper bounds for h^*-polynomials",
  "authors": [
    "Christian Haase",
    "Benjamin Nill",
    "Sam Payne"
  ],
  "comment": "AMS-LaTeX, 9 pages",
  "journal": "J. Reine Angew. Math. 637 (2009), 207-216",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "We give an effective upper bound on the h^*-polynomial of a lattice polytope in terms of its degree and leading coefficient, confirming a conjecture of Batyrev. We deduce this bound as a consequence of a strong Cayley decomposition theorem which says, roughly speaking, that any lattice polytope with a large multiple that has no interior lattice points has a nontrivial decomposition as a Cayley sum of polytopes of smaller dimension. In an appendix, we interpret this result in terms of adjunction theory for toric varieties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-23T09:15:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B20",
      "14M25",
      "14C20"
    ],
    "keywords": [
      "lattice polytope",
      "strong cayley decomposition theorem",
      "interior lattice points",
      "large multiple",
      "effective upper bound"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.3667H"
    }
  }
}