{
  "id": "math/0605787",
  "version": "v1",
  "published": "2006-05-31T17:59:04.000Z",
  "updated": "2006-05-31T17:59:04.000Z",
  "title": "On meromorphic functions defined by a differential system of order 1, II",
  "authors": [
    "Tristan Torrelli"
  ],
  "comment": "28 pages, 1 diagram",
  "categories": [
    "math.AG"
  ],
  "abstract": "Given a nonzero germ h of holomorphic function on (C^n,0), we study the condition: ``the ideal Ann\\_D 1/h is generated by operators of order 1''. When h defines a generic arrangement of hypersurfaces with an isolated singularity, we show that it is verified if and only if h is weighted homogeneous and -1 is the only integral root of its Bernstein-Sato polynomial. When h is a product, we give a process to test this last condition. Finally, we study some other related conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-05-31T17:59:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32C38",
      "32C38",
      "32S25",
      "14F10",
      "14F40"
    ],
    "keywords": [
      "meromorphic functions",
      "differential system",
      "bernstein-sato polynomial",
      "holomorphic function",
      "generic arrangement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......5787T"
    }
  }
}