{
  "id": "0903.3693",
  "version": "v3",
  "published": "2009-03-21T22:03:30.000Z",
  "updated": "2015-08-23T15:04:20.000Z",
  "title": "Structure of the cycle map for Hilbert schemes of families of nodal curves",
  "authors": [
    "Ziv Ran"
  ],
  "comment": "To appear in Israel J. Math. arXiv admin note: text overlap with arXiv:0803.4512",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study the relative Hilbert scheme of a family of nodal (or smooth) curves, over a base of arbitrary dimension, 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 determine the relevant cotangent sheaves and complexes. We determine the structure of certain projective bundles called node scrolls, which play an important role in the geometry of Hilbert schemes.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-08-13T06:46:23.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-08-23T15:04:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N99",
      "14H99"
    ],
    "keywords": [
      "cycle map",
      "nodal curves",
      "relevant cotangent sheaves",
      "relative symmetric product",
      "important role"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.3693R"
    }
  }
}