{
  "id": "math/0309374",
  "version": "v2",
  "published": "2003-09-23T07:02:49.000Z",
  "updated": "2003-12-11T08:26:39.000Z",
  "title": "On the irreducibility of multivariate subresultants",
  "authors": [
    "Laurent Busé",
    "Carlos D'Andrea"
  ],
  "comment": "Updated version, 4 pages, to appear in CRAS",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "Let $P_1,...,P_n$ be generic homogeneous polynomials in $n$ variables of degrees $d_1,...,d_n$ respectively. We prove that if $\\nu$ is an integer satisfying ${\\sum_{i=1}^n d_i}-n+1-\\min\\{d_i\\}<\\nu,$ then all multivariate subresultants associated to the family $P_1,...,P_n$ in degree $\\nu$ are irreducible. We show that the lower bound is sharp. As a byproduct, we get a formula for computing the residual resultant of $\\binom{\\rho-\\nu +n-1}{n-1}$ smooth isolated points in $\\PP^{n-1}.$",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-12-11T08:26:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "irreducibility",
      "generic homogeneous polynomials",
      "lower bound",
      "residual resultant",
      "smooth isolated points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......9374B"
    }
  }
}