{
  "id": "0807.0453",
  "version": "v3",
  "published": "2008-07-02T21:14:50.000Z",
  "updated": "2010-02-10T22:56:37.000Z",
  "title": "The rank of a hypergeometric system",
  "authors": [
    "Christine Berkesch"
  ],
  "comment": "32 pages. To appear in Compositio Mathematica. Revisions have been made to the exposition, and the notation has been simplified",
  "doi": "10.1112/S0010437X10004811",
  "categories": [
    "math.AG",
    "math.CO"
  ],
  "abstract": "The holonomic rank of the A-hypergeometric system M_A(\\beta) is the degree of the toric ideal I_A for generic parameters; in general, this is only a lower bound. To the semigroup ring of A we attach the ranking arrangement and use this algebraic invariant and the exceptional arrangement of nongeneric parameters to construct a combinatorial formula for the rank jump of M_A(\\beta). As consequences, we obtain a refinement of the stratification of the exceptional arrangement by the rank of M_A(\\beta) and show that the Zariski closure of each of its strata is a union of translates of linear subspaces of the parameter space. These results hold for generalized A-hypergeometric systems as well, where the semigroup ring of A is replaced by a nontrivial weakly toric module M contained in \\CC[\\ZZ A]. We also provide a direct proof of the result of M. Saito and W. Traves regarding the isomorphism classes of M_A(\\beta).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-02-10T22:56:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C70",
      "14M25",
      "16E30",
      "20M25",
      "13N10"
    ],
    "keywords": [
      "a-hypergeometric system",
      "exceptional arrangement",
      "nontrivial weakly toric module",
      "lower bound",
      "semigroup ring"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.0453B"
    }
  }
}