{
  "id": "math/0611903",
  "version": "v1",
  "published": "2006-11-29T09:25:59.000Z",
  "updated": "2006-11-29T09:25:59.000Z",
  "title": "Combinatorial structure of exceptional sets in resolutions of singularities",
  "authors": [
    "D. A. Stepanov"
  ],
  "comment": "18 pages; to appear as a preprint of the Max-Planck-Institut, Bonn",
  "categories": [
    "math.AG"
  ],
  "abstract": "The dual complex can be associated to any resolution of singularities whose exceptional set is a divisor with simple normal crossings. It generalizes to higher dimensions the notion of the dual graph of a resolution of surface singularity. The homotopy type of the dual complex does not depend on the choice of a resolution and thus can be considered as an invariant of singularity. In this preprint we show that the dual complex is homotopy trivial for resolutions of 3-dimensional terminal singularities and for resolutions of Brieskorn singularities. We also review our earlier results on resolutions of rational and hypersurface singularities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-11-29T09:25:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14B05",
      "32S50"
    ],
    "keywords": [
      "resolution",
      "exceptional set",
      "combinatorial structure",
      "dual complex",
      "simple normal crossings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11903S"
    }
  }
}