{
  "id": "2401.14951",
  "version": "v1",
  "published": "2024-01-26T15:35:28.000Z",
  "updated": "2024-01-26T15:35:28.000Z",
  "title": "Signature of the Milnor fiber of parametrized surfaces",
  "authors": [
    "R. Giménez Conejero",
    "Gergő Pintér"
  ],
  "comment": "36 pages, 7 figures, 1 table",
  "categories": [
    "math.AG"
  ],
  "abstract": "We compute the signature of the Milnor fiber of certain type of non-isolated complex surface singularities, namely, images of finitely determined holomorphic germs. An explicit formula is given in algebraic terms. As a corollary we show that the signature of the Milnor fiber is a topological invariant for these singularities. The proof combines complex analytic and smooth topological techniques. The main tools are Thom-Mather theory of map germs and the Ekholm-Sz\\H{u}cs-Takase-Saeki formula for immersions. We give a table with many examples for which the signature is computed using our formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-26T15:35:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S25",
      "32S50",
      "57R42"
    ],
    "keywords": [
      "milnor fiber",
      "parametrized surfaces",
      "non-isolated complex surface singularities",
      "map germs",
      "thom-mather theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}