{
  "id": "2308.05284",
  "version": "v1",
  "published": "2023-08-10T02:01:33.000Z",
  "updated": "2023-08-10T02:01:33.000Z",
  "title": "On invariants of a map germ from n-space to 2n-space",
  "authors": [
    "Juan José Nuño-Ballesteros",
    "Otoniel Nogueira da Silva",
    "João Nivaldo Tomazella"
  ],
  "categories": [
    "math.AG",
    "math.CV"
  ],
  "abstract": "We consider $\\mathcal{A}$-finite map germs $f$ from $(\\mathbb{C}^n,0)$ to $(\\mathbb{C}^{2n},0)$. First, we show that the number of double points that appears in a stabilization of $f$, denoted by $d(f)$, can be calculated as the length of the local ring of the double point set $D^2(f)$ of $f$, given by the Mond's ideal. In the case where $n\\leq 3$ and $f$ is quasihomogeneous, we also present a formula to calculate $d(f)$ in terms of the weights and degrees of $f$. Finally, we consider an unfolding $F(x,t) = (f_t(x),t)$ of $f$ and we find a set of invariants whose constancy in the family $f_t$ is equivalent to the Whitney equisingularity of $F$. As an application, we present a formula to calculate the Euler obstruction of the image of $f$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-10T02:01:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "invariants",
      "finite map germs",
      "whitney equisingularity",
      "monds ideal",
      "euler obstruction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}