{
  "id": "1409.4678",
  "version": "v1",
  "published": "2014-09-16T15:46:26.000Z",
  "updated": "2014-09-16T15:46:26.000Z",
  "title": "Characterization of curves in $C^{(2)}$",
  "authors": [
    "Meritxell Sáez"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper we characterize the irreducible curves lying in $C^{(2)}$. We prove that a curve $B$ has a degree one morphism to $C^{(2)}$ with image a curve of degree $d$ with irreducible preimage in $C\\times C$ if and only if there exists an irreducible smooth curve $D$ and morphisms from $D$ to $C$ and $B$ of degrees $d$ and $2$ respectively forming a diagram which does not reduce.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-16T15:46:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "characterization",
      "irreducible smooth curve",
      "irreducible curves",
      "irreducible preimage"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.4678S"
    }
  }
}