{
  "id": "math/9801048",
  "version": "v3",
  "published": "1998-01-11T06:22:36.000Z",
  "updated": "1998-04-11T17:24:51.000Z",
  "title": "Characteristic varieties of arrangements",
  "authors": [
    "Daniel C. Cohen",
    "Alexander I. Suciu"
  ],
  "comment": "LaTeX2e, 20 pages. A reference to Libgober's recent work in math.AG/9801070 is added. Several points are clarified, a new example is included",
  "journal": "Mathematical Proceedings of the Cambridge Philosophical Society 127 (1999), no. 1, 33-53",
  "doi": "10.1017/S0305004199003576",
  "categories": [
    "math.AG",
    "math.CO",
    "math.GT"
  ],
  "abstract": "The k-th Fitting ideal of the Alexander invariant B of an arrangement A of n complex hyperplanes defines a characteristic subvariety, V_k(A), of the complex algebraic n-torus. In the combinatorially determined case where B decomposes as a direct sum of local Alexander invariants, we obtain a complete description of V_k(A). For any arrangement A, we show that the tangent cone at the identity of this variety coincides with R^1_k(A), one of the cohomology support loci of the Orlik-Solomon algebra. Using work of Arapura and Libgober, we conclude that all positive-dimensional components of V_k(A) are combinatorially determined, and that R^1_k(A) is the union of a subspace arrangement in C^n, thereby resolving a conjecture of Falk. We use these results to study the reflection arrangements associated to monomial groups.",
  "revisions": [
    {
      "version": "v3",
      "updated": "1998-04-11T17:24:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M12",
      "52B30",
      "14H30",
      "20F36",
      "57M05"
    ],
    "keywords": [
      "arrangement",
      "characteristic varieties",
      "complex hyperplanes defines",
      "complex algebraic n-torus",
      "local alexander invariants"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Mathematical Proceedings of the Cambridge Philosophical Society",
      "year": 1999,
      "month": "Jul",
      "volume": 127,
      "number": 1,
      "pages": 33
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999MPCPS.127...33C"
    }
  }
}