{
  "id": "math/0410120",
  "version": "v1",
  "published": "2004-10-05T18:33:24.000Z",
  "updated": "2004-10-05T18:33:24.000Z",
  "title": "Geometry on nodal curves II: cycle map and intersection calculus",
  "authors": [
    "Ziv Ran"
  ],
  "comment": "32 pages amstex",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study the relative Hilbert scheme of a family of nodal (or smooth) curves via its (birational) cycle map, going to the relative symmetric product. We show the cycle map is the blowing up of the discriminant locus, which consists of cycles with multiple points. We derive an intersection calculus for Chern classes of tautological bundles on the relative Hilbert scheme, which has applications to enumerative geometry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-10-05T18:33:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N10",
      "14C05"
    ],
    "keywords": [
      "cycle map",
      "intersection calculus",
      "nodal curves",
      "relative hilbert scheme",
      "relative symmetric product"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10120R"
    }
  }
}