{
  "id": "1504.06169",
  "version": "v1",
  "published": "2015-04-23T13:12:40.000Z",
  "updated": "2015-04-23T13:12:40.000Z",
  "title": "The integer cohomology algebra of toric arrangements",
  "authors": [
    "Filippo Callegaro",
    "Emanuele Delucchi"
  ],
  "comment": "38 pages, 2 figures",
  "categories": [
    "math.AT",
    "math.CO"
  ],
  "abstract": "We compute the cohomology ring of the complement of a toric arrangement with integer coefficients and investigate its dependency from the arrangement's combinatorial data. To this end, we study a morphism of spectral sequences associated to certain combinatorially defined subcomplexes of the toric Salvetti category in the complexified case, and use a technical argument in order to extend the results to full generality. As a byproduct we obtain: -a \"combinatorial\" version of Brieskorn's lemma in terms of Salvetti complexes of complexified arrangements, -a uniqueness result for realizations of arithmetic matroids with at least one basis of multiplicity 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-23T13:12:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integer cohomology algebra",
      "toric arrangement",
      "arrangements combinatorial data",
      "toric salvetti category",
      "uniqueness result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150406169C"
    }
  }
}