{
  "id": "math/0601640",
  "version": "v3",
  "published": "2006-01-26T13:38:57.000Z",
  "updated": "2007-11-21T12:33:53.000Z",
  "title": "An algebraic formula for the index of a vector field on an isolated complete intersection singularity",
  "authors": [
    "H. -Chr. Graf von Bothmer",
    "W. Ebeling",
    "X. Gomez-Mont"
  ],
  "comment": "18 pages; added an example which is not quasi homogeneous. A script calculating this example can be found at http://www.iag.uni-hannover.de/~bothmer/gobelin/ or at the and of the source file of this article",
  "journal": "Annales de l'Institut Fourier, Vol. 58 no. 5 (2008), p. 1761-1783",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "Let (V,0) be a germ of a complete intersection variety in \\CC^{n+k}, n>0, having an isolated singularity at 0 and X be the germ of a holomorphic vector field on \\CC^{n+k} tangent to V and having on V an isolated zero at 0. We show that in this case the homological index and the GSV-index coincide. In the case when the zero of X is also isolated in the ambient space \\CC^{n+k} we give a formula for the homological index in terms of local linear algebra.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-11-21T12:33:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14B05",
      "32S10",
      "13D25"
    ],
    "keywords": [
      "isolated complete intersection singularity",
      "algebraic formula",
      "complete intersection variety",
      "holomorphic vector field",
      "homological index"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1640C"
    }
  }
}