{
  "id": "0803.1743",
  "version": "v2",
  "published": "2008-03-12T10:54:43.000Z",
  "updated": "2008-09-12T11:13:15.000Z",
  "title": "Poincare series of filtrations corresponding to ideals on surfaces",
  "authors": [
    "A. Campillo",
    "F. Delgado",
    "S. M. Gusein-Zade"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Earlier the authors considered and, in some cases, computed Poincare series of two sorts of multi-index filtrations on the ring of germs of functions on a complex (normal) surface singularity (in particular on the complex plane). A filtration from the first class was defined by a curve (with several branches) on the surface singularity. The other one (so called divisorial filtration) was defined by a set of components of the exceptional divisor of a modification of the surface singularity. Here we define a filtration corresponding to an ideal or to a set of ideals in the ring of germs of functions on a surface singularity and compute the corresponding Poincare series in some cases. For the complex plane this notion unites the two classes of filtrations described above.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-09-12T11:13:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J17",
      "32S25"
    ],
    "keywords": [
      "surface singularity",
      "filtrations corresponding",
      "complex plane",
      "multi-index filtrations",
      "first class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.1743C"
    }
  }
}