{
  "id": "math/0603476",
  "version": "v1",
  "published": "2006-03-20T09:24:06.000Z",
  "updated": "2006-03-20T09:24:06.000Z",
  "title": "On Abel maps of stable curves",
  "authors": [
    "Lucia Caporaso",
    "Eduardo Esteves"
  ],
  "comment": "32 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We construct Abel maps for a stable curve $X$. Namely, for each one-parameter deformation of $X$ with regular total space, and every integer $d>0$, we construct by specialization a map $\\alpha^d_X$ from the smooth locus of $X^d$ to the moduli scheme of balanced line bundles on semistable curves over $X$. For $d=1$, we show that $\\alpha^1_X$ naturally extends over $X$, and does not depend on the choice of the deformation; we give a precise description of when it is injective.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-20T09:24:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10"
    ],
    "keywords": [
      "stable curve",
      "construct abel maps",
      "regular total space",
      "precise description",
      "one-parameter deformation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3476C"
    }
  }
}