{
  "id": "2012.11846",
  "version": "v1",
  "published": "2020-12-22T06:03:53.000Z",
  "updated": "2020-12-22T06:03:53.000Z",
  "title": "Normal polytopes and ellipsoids",
  "authors": [
    "Joseph Gubeladze"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "We show that: (1) unimodular simplices in a lattice 3-polytope cover a neighborhood of the boundary of the polytope if and only if the polytope is very ample, (2) the convex hull of lattice points in every ellipsoid in R^3 has a unimodular cover, and (3) for every d at least 6, there are ellipsoids in R^d, such that the convex hulls of the lattice points in these ellipsoids are not even normal. Part (3) answers a question of Bruns, Michalek, and the author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-22T06:03:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B20",
      "11H06"
    ],
    "keywords": [
      "normal polytopes",
      "convex hull",
      "lattice points",
      "unimodular cover",
      "unimodular simplices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}