{
  "id": "0810.4129",
  "version": "v1",
  "published": "2008-10-22T18:16:09.000Z",
  "updated": "2008-10-22T18:16:09.000Z",
  "title": "The cohomology of line bundles of splice-quotient singularities",
  "authors": [
    "András Némethi"
  ],
  "comment": "16 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We provide several results on splice-quotient singularities: a combinatorial expression of the dimension of the first cohomology of all `natural' line bundles, an equivariant Campillo-Delgado-Gusein-Zade type formula about the dimension of relative sections of line bundles (proving that the equivariant, divisorial multi-variable Hilbert series is topological), a combinatorial description of divisors of analytic function-germs, and an expression for the multiplicity of the singularity from its resolution graph. Additional, we establish a new formula for the Seiberg-Witten invariants of any rational homology sphere singularity link.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-22T18:16:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S05",
      "32S25",
      "57M27",
      "32S45",
      "32S50",
      "32C35",
      "57R57"
    ],
    "keywords": [
      "line bundles",
      "splice-quotient singularities",
      "rational homology sphere singularity link",
      "equivariant campillo-delgado-gusein-zade type formula",
      "divisorial multi-variable hilbert series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.4129N"
    }
  }
}