{
  "id": "0808.1821",
  "version": "v1",
  "published": "2008-08-13T12:43:17.000Z",
  "updated": "2008-08-13T12:43:17.000Z",
  "title": "Relations between the leading terms of a polynomial automorphism",
  "authors": [
    "Philippe Bonnet",
    "Stéphane Vénéreau"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $I$ be the ideal of relations between the leading terms of the polynomials defining an automorphism of $K^n$. In this paper, we prove the existence of a locally nilpotent derivation which preserves $I$. Moreover, if $I$ is principal, i.e. $I=(R)$, we compute an upper bound for $\\deg_2(R)$ for some degree function $\\deg_2$ defined by the automorphism. As applications, we determine all the principal ideals of relations for automorphisms of $K^3$ and deduce two elementary proofs of the Jung-van der Kulk Theorem about the tameness of automorphisms of $K^{2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-08-13T12:43:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14R10"
    ],
    "keywords": [
      "leading terms",
      "polynomial automorphism",
      "jung-van der kulk theorem",
      "degree function",
      "principal ideals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.1821B"
    }
  }
}