{
  "id": "1309.5682",
  "version": "v1",
  "published": "2013-09-23T02:10:42.000Z",
  "updated": "2013-09-23T02:10:42.000Z",
  "title": "Variation of the canonical height in a family of rational maps",
  "authors": [
    "Dragos Ghioca",
    "Niki Myrto Mavraki"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $d\\ge 2$ be an integer, let $c(t)$ be any rational map, and let $f_t(z) := (z^d+t)/z$ be a family of rational maps indexed by t. For each algebraic number $t$, we let $h_{f_t}(c(t))$ be the canonical height of $c(t)$ with respect to the rational map $f_t$. We prove that the map $H(t):=h_{f_t}(c(t))$ (as $t$ varies among the algebraic numbers) is a Weil height.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-23T02:10:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "canonical height",
      "algebraic number",
      "weil height",
      "rational maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.5682G"
    }
  }
}