{
  "id": "2202.10909",
  "version": "v1",
  "published": "2022-02-22T14:18:05.000Z",
  "updated": "2022-02-22T14:18:05.000Z",
  "title": "Integral points of bounded height on a certain toric variety",
  "authors": [
    "Florian Wilsch"
  ],
  "comment": "25 pages, 4 figures",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We determine an asymptotic formula for the number of integral points of bounded height on a certain toric variety, which is incompatible with part of a preprint by Chambert-Loir and Tschinkel. We provide an alternative interpretation of the asymptotic formula we get. To do so, we construct an analogue of Peyre's constant $\\alpha$ and describe its relation to a new obstruction to the Zariski density of integral points in certain regions of varieties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-22T14:18:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D45",
      "11G35",
      "14G05"
    ],
    "keywords": [
      "integral points",
      "toric variety",
      "bounded height",
      "asymptotic formula",
      "peyres constant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}