{
  "id": "1003.3241",
  "version": "v2",
  "published": "2010-03-16T20:22:06.000Z",
  "updated": "2010-04-26T16:51:38.000Z",
  "title": "Height bound and preperiodic points for jointly regular families of rational maps",
  "authors": [
    "ChongGyu Lee"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Silverman proved a height inequality for jointly regular family of rational maps and the author improved it for jointly regular pairs. In this paper, we provide the same improvement for jointly regular family; if S is a jointly regular set of rational maps, then \\sum_{f\\in S} \\dfrac{1}{\\deg f} h\\bigl(f(P) \\bigr) > (1+ \\dfrac{1}{r}) f(P) - C where r = \\max_{f\\in S} r(f).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-04-26T16:51:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G50",
      "37P30",
      "32H50",
      "37P05"
    ],
    "keywords": [
      "jointly regular family",
      "rational maps",
      "preperiodic points",
      "height bound",
      "height inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.3241L"
    }
  }
}