{
  "id": "0705.0906",
  "version": "v1",
  "published": "2007-05-07T13:53:19.000Z",
  "updated": "2007-05-07T13:53:19.000Z",
  "title": "Remarks on families of singular curves with hyperelliptic normalizations",
  "authors": [
    "Andreas Leopold Knutsen"
  ],
  "comment": "18 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We give restrictions on the existence of families of curves on smooth projective surfaces $S$ of nonnegative Kodaira dimension all having constant geometric genus $g \\geq 2$ and hyperelliptic normalizations. In particular, we prove a Reider-like result whose proof is ``vector bundle-free'' and relies on deformation theory and bending-and-breaking of rational curves in $\\Sym^2(S)$. We also give examples of families of such curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-05-07T13:53:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10",
      "14E30",
      "14H51",
      "14J10"
    ],
    "keywords": [
      "hyperelliptic normalizations",
      "singular curves",
      "constant geometric genus",
      "smooth projective surfaces",
      "rational curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.0906L"
    }
  }
}