{
  "id": "math/0306195",
  "version": "v2",
  "published": "2003-06-11T21:41:29.000Z",
  "updated": "2003-07-24T19:42:48.000Z",
  "title": "Equations of Parametric Surfaces with Base Points via Syzygies",
  "authors": [
    "William Adkins",
    "J. William Hoffman",
    "Hao Hao Wang"
  ],
  "comment": "22 pages. Revised version adds proofs that were originally quoted from Hoffman and Wang (arxiv.,org/abs/math.AG/0305125). The paper of Hoffman and Wang has now been withdrawn",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $S$ be a parametric surface in $\\proj{3}$ given as the image of $\\phi: \\proj{1} \\times \\proj{1} \\to \\proj{3}$. This paper will show that the use of syzygies in the form of a combination of moving planes and moving quadrics provides a valid method for finding the implicit equation of $S$ when certain base points are present. This work extends the algorithm provided by Cox for when $\\phi$ has no base points, and it is an analogous to some of the results of Bus\\'{e}, Cox and D'Andrea for the case when $\\phi: \\proj{2} \\to \\proj{3}$ has base points.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-07-24T19:42:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14Q10",
      "13D02",
      "14Q05"
    ],
    "keywords": [
      "base points",
      "parametric surface",
      "implicit equation",
      "valid method",
      "work extends"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......6195A"
    }
  }
}