{
  "id": "1408.5416",
  "version": "v1",
  "published": "2014-08-22T20:12:29.000Z",
  "updated": "2014-08-22T20:12:29.000Z",
  "title": "Variation of the canonical height for polynomials in several variables",
  "authors": [
    "Patrick Ingram"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let K be a number field, X/K a curve, and f/X a family of endomorphisms of projective N-space. It follows from a result of Call and Silverman that the canonical height associated to the family f, evaluated along a section, differs from a Weil height on the base by little-o of a Weil height. In the case where f is a family with an invariant hyperplane, whose restriction to this invariant hyperplane is isotrivial, we improve this by showing that the canonical height along a section differs from a Weil height on the base by a bounded amount.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-22T20:12:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37P30"
    ],
    "keywords": [
      "canonical height",
      "weil height",
      "polynomials",
      "invariant hyperplane",
      "number field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.5416I"
    }
  }
}