{
  "id": "0907.0212",
  "version": "v2",
  "published": "2009-07-01T17:46:06.000Z",
  "updated": "2010-06-01T22:24:35.000Z",
  "title": "A Riemann singularity theorem for integral curves",
  "authors": [
    "Sebastian Casalaina-Martin",
    "Jesse Leo Kass"
  ],
  "comment": "23 pages, AMS Latex, improved exposition, to appear in the Amer. J. Math",
  "categories": [
    "math.AG"
  ],
  "abstract": "We prove results generalizing the classical Riemann Singularity Theorem to the case of integral, singular curves. The main result is a computation of the multiplicity of the theta divisor of an integral, nodal curve at an arbitrary point. We also conjecture a general formula for the multiplicity of points on the theta divisor of a singular integral curve and present some evidence for this conjecture. Our results give a partial answer to a question posed by Lucia Caporaso in a recent paper.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-06-01T22:24:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H40",
      "14H42",
      "14H20",
      "14K25"
    ],
    "keywords": [
      "theta divisor",
      "classical riemann singularity theorem",
      "singular integral curve",
      "arbitrary point",
      "singular curves"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.0212C"
    }
  }
}