{
  "id": "math/0211253",
  "version": "v1",
  "published": "2002-11-16T22:37:37.000Z",
  "updated": "2002-11-16T22:37:37.000Z",
  "title": "Resonant local systems on complements of discriminantal arrangements and sl_2 representations",
  "authors": [
    "Daniel C. Cohen",
    "Alexander N. Varchenko"
  ],
  "comment": "LaTeX, 12 pages",
  "journal": "Geom. Dedicata 101 (2003), 217-234",
  "categories": [
    "math.AG",
    "math.CO",
    "math.QA"
  ],
  "abstract": "We calculate the skew-symmetric cohomology of the complement of a discriminantal hyperplane arrangement with coefficients in local systems arising in the context of the representation theory of the Lie algebra sl_2. For a discriminantal arrangement in C^k, the skew-symmetric cohomology is nontrivial in dimension k-1 precisely when the \"master function\" which defines the local system on the complement has nonisolated critical points. In symmetric coordinates, the critical set is a union of lines. Generically, the dimension of this nontrivial skew-symmetric cohomology group is equal to the number of critical lines.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-11-16T22:37:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "32S22",
      "52C35",
      "55N25"
    ],
    "keywords": [
      "resonant local systems",
      "discriminantal arrangement",
      "complement",
      "nontrivial skew-symmetric cohomology group",
      "discriminantal hyperplane arrangement"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....11253C"
    }
  }
}