{
  "id": "1809.02001",
  "version": "v1",
  "published": "2018-09-06T14:08:42.000Z",
  "updated": "2018-09-06T14:08:42.000Z",
  "title": "Rational approximations on toric varieties",
  "authors": [
    "Zhizhong Huang"
  ],
  "comment": "Preliminary version. Comments are welcome!",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Using universal torsor method due to Salberger, we study the approximation of a general fixed point by rational points on split toric varieties. We prove that under certain hypothesis the best approximations can be achieved on rational curves passing through the fixed point of minimal degree, confirming a conjecture of McKinnon. These curves correspond, according to Batyrev's terminology, to the minimal centred primitive collections of the fan.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-06T14:08:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rational approximations",
      "universal torsor method",
      "split toric varieties",
      "minimal centred primitive collections",
      "general fixed point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}