{
  "id": "math/0210096",
  "version": "v2",
  "published": "2002-10-07T08:09:28.000Z",
  "updated": "2003-02-11T18:52:54.000Z",
  "title": "On the closed image of a rational map and the implicitization problem",
  "authors": [
    "Laurent Buse",
    "Jean-Pierre Jouanolou"
  ],
  "comment": "43 pages, revised version. To appear in Journal of Algebra",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "In this paper, we investigate some topics around the closed image $S$ of a rational map $\\lambda$ given by some homogeneous elements $f_1,...,f_n$ of the same degree in a graded algebra $A$. We first compute the degree of this closed image in case $\\lambda$ is generically finite and $f_1,...,f_n$ define isolated base points in $\\Proj(A)$. We then relate the definition ideal of $S$ to the symmetric and the Rees algebras of the ideal $I=(f_1,...,f_n) \\subset A$, and prove some new acyclicity criteria for the associated approximation complexes. Finally, we use these results to obtain the implicit equation of $S$ in case $S$ is a hypersurface, $\\Proj(A)=\\PP^{n-2}_k$ with $k$ a field, and base points are either absent or local complete intersection isolated points.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-02-11T18:52:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14Qxx",
      "13D02"
    ],
    "keywords": [
      "closed image",
      "rational map",
      "implicitization problem",
      "local complete intersection isolated points",
      "define isolated base points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10096B"
    }
  }
}