{
  "id": "0809.3443",
  "version": "v2",
  "published": "2008-09-19T19:20:30.000Z",
  "updated": "2008-09-26T23:26:14.000Z",
  "title": "Hodge spectrum of hyperplane arrangements",
  "authors": [
    "Nero Budur"
  ],
  "comment": "v2: added references to Prof. Libgober's work",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this article there are two main results. The first result gives a formula, in terms of a log resolution, for the graded pieces of the Hodge filtration on the cohomology of a unitary local system of rank one on the complement of an arbitrary divisor in a smooth projective complex variety. The second result is an application of the first. We give a combinatorial formula for the spectrum of a hyperplane arrangement. M. Saito recently proved that the spectrum of a hyperplane arrangement depends only on combinatorics. However, a combinatorial formula was missing. The formula is achieved by a different method.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-09-26T23:26:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14B05",
      "32S35",
      "32S22"
    ],
    "keywords": [
      "hodge spectrum",
      "combinatorial formula",
      "smooth projective complex variety",
      "hyperplane arrangement depends",
      "unitary local system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.3443B"
    }
  }
}