{
  "id": "2305.00307",
  "version": "v1",
  "published": "2023-04-29T17:28:30.000Z",
  "updated": "2023-04-29T17:28:30.000Z",
  "title": "Homotopy stability of spaces of non-resultant systems of bounded multiplicity with real coefficients",
  "authors": [
    "Andrzej Kozlowski",
    "Kohhei Yamaguchi"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2212.05494",
  "categories": [
    "math.AT"
  ],
  "abstract": "We continue our study of the topology of the spaces of $m$ tuples of real polynomials with common degree $d$ and without common roots of multiplicity $n$, and in particular their stability properties with respect to $d$. In an earlier paper we have proved a homotopy stability result and determined the stable homotopy types of such spaces in the case $m n >=4$. In the case $m n= 3$ we could only prove stability in homology. In this paper we prove the corresponding homotopy result for the case $(m,n)=(3,1)$. in the appendix we also deal with the case ${m,n)={1,2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-29T17:28:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P15",
      "55R80",
      "55P35"
    ],
    "keywords": [
      "non-resultant systems",
      "real coefficients",
      "bounded multiplicity",
      "homotopy stability result",
      "common roots"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}