{
  "id": "1612.06793",
  "version": "v1",
  "published": "2016-12-20T18:25:40.000Z",
  "updated": "2016-12-20T18:25:40.000Z",
  "title": "The homotopy type of spaces of resultants of bounded multiplicity",
  "authors": [
    "Andrzej Kozlowski",
    "Kohhei Yamaguchi"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "For positive integers $m,n, d\\geq 1$ with $(m,n)\\not= (1,1)$ and a field $\\Bbb F$ with its algebraic closure $\\overline{\\Bbb F}$, let $\\text{Poly}^{d,m}_n(\\Bbb F)$ denote the space of all $m$-tuples $(f_1(z),\\cdots ,f_m(z))\\in \\Bbb F [z]$ of monic polynomials of the same degree $d$ such that polynomials $f_1(z),\\cdots ,f_m(z)$ have no common root in $\\overline{\\Bbb F}$ of multiplicity $\\geq n$. These spaces were defined by Farb and Wolfson in \\cite{FW} as generalizations of spaces first studied by Arnold, Vassiliev, Segal and others in different contexts. In \\cite{FW} they obtained algebraic geometrical and arithmetic results about the topology of these spaces. In this paper we investigate the homotopy type of these spaces for the case $\\Bbb F =\\mathbb{C}$. Our results generalize those of \\cite{FW} for $\\Bbb F =\\Bbb C$ and also results of G. Segal \\cite{Se}, V. Vassiliev \\cite{Va} and F.Cohen-R.Cohen-B.Mann-R.Milgram \\cite{CCMM} for $m\\geq 2$ and $n\\geq 2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-20T18:25:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P10",
      "55R80",
      "55P35"
    ],
    "keywords": [
      "homotopy type",
      "bounded multiplicity",
      "resultants",
      "algebraic closure",
      "spaces first"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}