{
  "id": "0906.1991",
  "version": "v3",
  "published": "2009-06-10T18:52:29.000Z",
  "updated": "2010-01-10T08:19:52.000Z",
  "title": "The Monodromy Conjecture for hyperplane arrangements",
  "authors": [
    "Nero Budur",
    "Mircea Mustata",
    "Zach Teitler"
  ],
  "comment": "Added: 2.6-2.9 discussing the p-adic case",
  "categories": [
    "math.AG"
  ],
  "abstract": "The Monodromy Conjecture asserts that if c is a pole of the local topological zeta function of a hypersurface, then exp(2\\pi i c) is an eigenvalue of the monodromy on the cohomology of the Milnor fiber. A stronger version of the conjecture asserts that every pole is a root of the Bernstein-Sato polynomial of the hypersurface. In this note we prove the weak version of the conjecture for hyperplane arrangements. Furthermore, we reduce the strong version to the following conjecture: -n/d is always a root of the Bernstein-Sato polynomial of an indecomposable essential central hyperplane arrangement of d hyperplanes in the affine n-space.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-01-10T08:19:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S40",
      "32S22"
    ],
    "keywords": [
      "bernstein-sato polynomial",
      "indecomposable essential central hyperplane arrangement",
      "local topological zeta function",
      "monodromy conjecture asserts",
      "milnor fiber"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.1991B"
    }
  }
}