{
  "id": "1102.5024",
  "version": "v2",
  "published": "2011-02-24T16:05:13.000Z",
  "updated": "2013-05-07T18:24:09.000Z",
  "title": "A geometric construction of Coxeter-Dynkin diagrams of bimodal singularities",
  "authors": [
    "Wolfgang Ebeling",
    "David Ploog"
  ],
  "comment": "18 pages, 8 figures. The published version lists four equations in Table 4 which are not quasismooth. We thank Kazushi Ueda for this observation. In the new version, the equations have been corrected; the results hold without changes",
  "journal": "Manuscripta Mathematica 140 (2013), 195-212",
  "categories": [
    "math.AG"
  ],
  "abstract": "We consider the Berglund-H\\\"ubsch transpose of a bimodal invertible polynomial and construct a triangulated category associated to the compactification of a suitable deformation of the singularity. This is done in such a way that the corresponding Grothendieck group with the (negative) Euler form can be described by a graph which corresponds to the Coxeter-Dynkin diagram with respect to a distinguished basis of vanishing cycles of the bimodal singularity.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-07T18:24:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S25",
      "18E30",
      "53D37"
    ],
    "keywords": [
      "bimodal singularity",
      "coxeter-dynkin diagram",
      "geometric construction",
      "corresponding grothendieck group",
      "euler form"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.5024E"
    }
  }
}