{
  "id": "1110.5580",
  "version": "v3",
  "published": "2011-10-24T13:41:10.000Z",
  "updated": "2011-11-28T15:49:12.000Z",
  "title": "Codimension Two Determinantal Varieties with Isolated Singularities",
  "authors": [
    "Miriam da Silva Pereira",
    "Maria Aparecida Soares Ruas"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "We study codimension two determinantal varieties with isolated singularities. These singularities admit a unique smoothing, thus we can define their Milnor number as the middle Betti number of their generic fiber. For surfaces in C^4, we obtain a L\\^e-Greuel formula expressing the Milnor number of the surface in terms of the second polar multiplicity and the Milnor number of a generic section. We also relate the Milnor number with Ebeling and Gusein-Zade index of the 1- form given by the differential of a generic linear projection defined on the surface. To illustrate the results, in the last section we compute the Milnor number of some normal forms from A. Fr\\\"uhbis-Kr\\\"uger and A. Neumer [2] list of simple determinantal surface singularities.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-11-28T15:49:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "milnor number",
      "determinantal varieties",
      "isolated singularities",
      "simple determinantal surface singularities",
      "generic linear projection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.5580D"
    }
  }
}