{
  "id": "math/0104266",
  "version": "v1",
  "published": "2001-04-27T17:39:35.000Z",
  "updated": "2001-04-27T17:39:35.000Z",
  "title": "Clifford Index of ACM Curves in ${\\mathbb P}^3$",
  "authors": [
    "Robin Hartshorne"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper we review the notions of gonality and Clifford index of an abstract curve. For a curve embedded in a projective space, we investigate the connection between the \\ci of the curve and the \\gc al properties of its \\emb. In particular if $C$ is a curve of degree $d$ in ${\\P}^3$, and if $L$ is a multisecant of maximum order $k$, then the pencil of planes through $L$ cuts out a $g^1_{d-k}$ on $C$. If the gonality of $C$ is equal to $d-k$ we say the gonality of $C$ can be computed by multisecants. We discuss the question whether the \\go of every smooth ACM curve in ${\\P}^3$ can be computed by multisecants, and we show the answer is yes in some special cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-04-27T17:39:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H45",
      "14H50",
      "14M06"
    ],
    "keywords": [
      "clifford index",
      "multisecant",
      "smooth acm curve",
      "maximum order",
      "abstract curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......4266H"
    }
  }
}