{
  "id": "2005.04505",
  "version": "v1",
  "published": "2020-05-09T19:55:07.000Z",
  "updated": "2020-05-09T19:55:07.000Z",
  "title": "Equisingularity of families of functions on isolated determinantal singularities",
  "authors": [
    "Rafaela S. Carvalho",
    "Juan J. Nuño-Ballesteros",
    "Bruna Oréfice-Okamoto",
    "João N. Tomazella"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "We study the equisingularity of a family of function germs $\\{f_t\\colon(X_t,0)\\to (\\mathbb{C},0)\\}$, where $(X_t,0)$ are $d$-dimensional isolated determinantal singularities. We define the $(d-1)$th polar multiplicity of the fibers $X_t\\cap f_t^{-1}(0)$ and we show how the constancy of the polar multiplicities is related to the constancy of the Milnor number of $f_t$ and the Whitney equisingularity of the family.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-09T19:55:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S15",
      "32S30",
      "58K60"
    ],
    "keywords": [
      "dimensional isolated determinantal singularities",
      "th polar multiplicity",
      "whitney equisingularity",
      "milnor number",
      "function germs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}