{
  "id": "0807.0574",
  "version": "v1",
  "published": "2008-07-03T14:26:02.000Z",
  "updated": "2008-07-03T14:26:02.000Z",
  "title": "Equisingularity and The Euler Characteristic of a Milnor Fibre",
  "authors": [
    "Kevin Houston"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AG",
    "math.CV"
  ],
  "abstract": "We study the Euler characteristic of the Milnor fibre of a hypersurface singularity. This invariant is given in terms of the Euler characteristic of a fibre in between the original singularity and its Milnor fibre and in terms of the Euler characteristics associated to strata of the in-between fibre. From this we can deduce a result of Massey and Siersma regarding singularities with a one-dimensional critical locus. The result is also applied to the study of equisingularity. The famous Brian\\c{c}on-Speder-Teissier result states that a family of isolated hypersurface singularities is equisingular if and only if its $\\mu ^*$-sequence is constant. We show that if a similar sequence for a family of corank 1 complex analytic mappings from n-space to (n+1)-space is constant, then the image of the family of mappings is equisingular. For families of corank 1 maps from 3-space to 4-space we show that the converse is true also.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-07-03T14:26:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14B07",
      "32S55",
      "32S15",
      "32S30"
    ],
    "keywords": [
      "euler characteristic",
      "milnor fibre",
      "equisingularity",
      "hypersurface singularity",
      "complex analytic mappings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.0574H"
    }
  }
}