{
  "id": "2408.13258",
  "version": "v1",
  "published": "2024-08-02T01:19:34.000Z",
  "updated": "2024-08-02T01:19:34.000Z",
  "title": "Height functions on singular surfaces parameterized by smooth maps $\\mathcal{A}$-equivalent to $S_k$, $B_k$, $C_k$ and $F_4$",
  "authors": [
    "Toshizumi Fukui",
    "Masaru Hasegawa"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:2408.00231",
  "categories": [
    "math.DG"
  ],
  "abstract": "We describe singularities of height functions on singular surfaces in $\\mathbb{R}^3$ parameterized by smooth map-germs $\\mathcal{A}$-equivalent to one of $S_k$, $B_k$, $C_k$ and $F_4$ singularities in terms of extended geometric language via finite succession of blowing-ups. We investigate singularities of dual surfaces of such singular surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-02T01:19:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singular surfaces",
      "height functions",
      "smooth maps",
      "equivalent",
      "singularities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}