{
  "id": "math/0406621",
  "version": "v2",
  "published": "2004-06-30T15:07:16.000Z",
  "updated": "2004-08-16T21:18:46.000Z",
  "title": "On the Degree Growth of Birational Mappings in Higher Dimension",
  "authors": [
    "Eric Bedford",
    "Kyounghee Kim"
  ],
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "Let $f$ be a birational map of ${\\bf C}^d$, and consider the degree complexity, or asymptotic degree growth rate $\\delta(f)=\\lim_{n\\to\\infty}({\\rm deg}(f^n))^{1/n}$. We introduce a family of elementary maps, which have the form $f=L\\circ J$, where $L$ is (invertible) linear, and $J(x_1,...,x_d)=(x_1^{-1},...,x_d^{-1})$. We develop a method of regularization and show how it can be used to compute $\\delta$ for an elementary map.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-08-16T21:18:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F99",
      "32H50",
      "14E07"
    ],
    "keywords": [
      "birational mappings",
      "higher dimension",
      "elementary map",
      "asymptotic degree growth rate",
      "degree complexity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......6621B"
    }
  }
}