{
  "id": "math/0112321",
  "version": "v1",
  "published": "2001-12-05T00:00:00.000Z",
  "updated": "2001-12-05T00:00:00.000Z",
  "title": "Abeliants and their application to an elementary construction of Jacobians",
  "authors": [
    "Greg W. Anderson"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "The {\\em abeliant} is a polynomial rule for producing an $n$ by $n$ matrix with entries in a given ring from an $n$ by $n$ by $n+2$ array of elements of that ring. The theory of abeliants, first introduced in an earlier paper of the author, is redeveloped here in a simpler way. Then this theory is exploited to give an explicit elementary construction of the Jacobian of a nonsingular projective algebraic curve defined over an algebraically closed field. The standard of usefulness and aptness we strive toward is that set by Mumford's elementary construction of the Jacobian of a hyperelliptic curve. This paper has appeared as Advances in Math 172 (2002) 169-205.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-12-05T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "application",
      "explicit elementary construction",
      "mumfords elementary construction",
      "nonsingular projective algebraic curve",
      "simpler way"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....12321A"
    }
  }
}