{
  "id": "0704.1367",
  "version": "v1",
  "published": "2007-04-11T08:29:44.000Z",
  "updated": "2007-04-11T08:29:44.000Z",
  "title": "On families of rational curves in the Hilbert square of a surface (with an Appendix by Edoardo Sernesi)",
  "authors": [
    "Flaminio Flamini",
    "Andreas Leopold Knutsen",
    "Gianluca Pacienza",
    "Edoardo Sernesi"
  ],
  "comment": "Submitted preprint. Paper 1: On families of rational curves in the Hilbert square of a surface (with an Appendix by Edoardo Sernesi). Authors: Flaminio Flamini, Andreas Leopold Knutsen and Gianluca Pacienza. Pages: 1 -- 34. Figures: 1. Paper 2: Partial desingularizations of families of nodal curves. Author: Edoardo Sernesi. Pages: 35--37",
  "categories": [
    "math.AG"
  ],
  "abstract": "Under natural hypotheses we give an upper bound on the dimension of families of singular curves with hyperelliptic normalizations on a surface S with p_g(S) >0 via the study of the associated families of rational curves in Hilb^2(S). We use this result to prove the existence of nodal curves of geometric genus 3 with hyperelliptic normalizations, on a general K3 surface, thus obtaining specific 2-dimensional families of rational curves in its Hilbert square. We describe two infinite series of examples of general, primitively polarized K3's such that their Hilbert squares contain a IP^2 or a threefold birational to a IP^1-bundle over a K3. We discuss some consequences on the Mori cone of the Hilbert square of a general K3.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-04-11T08:29:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10",
      "14H51",
      "14J28",
      "14C05",
      "14C25",
      "14D15",
      "14E30"
    ],
    "keywords": [
      "rational curves",
      "edoardo sernesi",
      "hyperelliptic normalizations",
      "general k3 surface",
      "hilbert squares contain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.1367F"
    }
  }
}