{
  "id": "math/9805005",
  "version": "v2",
  "published": "1998-05-01T14:44:06.000Z",
  "updated": "1998-09-03T22:35:12.000Z",
  "title": "The A-hypergeometric System Associated with a Monomial Curve",
  "authors": [
    "Eduardo Cattani",
    "Carlos D'Andrea",
    "Alicia Dickenstein"
  ],
  "comment": "Plain Tex, 29 pages. Revised version to appear in Duke Math. J. Several new results have been added",
  "journal": "Duke Mathematical Journal, Vol. 99, No. 2, 179-207 (1999)",
  "categories": [
    "math.AG"
  ],
  "abstract": "We make a detailed analysis of the A-hypergeometric system (or GKZ system) associated with a monomial curve and integral, hence resonant, exponents. We characterize the Laurent polynomial solutions and show that these are the only rational solutions. We also show that for any exponent, there are at most two linearly independent Laurent solutions, and that the upper bound is reached if and only if the curve is not arithmetically Cohen--Macaulay. We then construct, for all integral parameters, a basis of local solutions in terms of the roots of the generic univariate polynomial associated with A. We determine the holonomic rank r for all integral exponents and show that it is constantly equal to the degree d of X if and only if X is arithmetically Cohen-Macaulay. Otherwise there is at least one exponent for which r = d + 1.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1998-09-03T22:35:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C70",
      "14M05",
      "33D20"
    ],
    "keywords": [
      "a-hypergeometric system",
      "monomial curve",
      "linearly independent laurent solutions",
      "generic univariate polynomial",
      "arithmetically cohen-macaulay"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "Plain TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......5005C"
    }
  }
}