{
  "id": "2005.12817",
  "version": "v1",
  "published": "2020-05-26T15:47:46.000Z",
  "updated": "2020-05-26T15:47:46.000Z",
  "title": "Bounds on the dimension of linear series on stable curves",
  "authors": [
    "Karl Christ"
  ],
  "comment": "23 pages, 4 Figures",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study the dimension of linear series on stable curves. In the first part, we show that a general linear series with semistable multidegree is not special, and obtain results on the dimension of the special loci in the Picard scheme. In the process, we give a new characterization of semistability when the total degree equals the genus of the curve. In the second part, we give a generalization of Clifford's inequality to linear series of uniform multidegree and show that the new bound is achieved on every stable curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-26T15:47:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stable curve",
      "general linear series",
      "total degree equals",
      "special loci",
      "picard scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}