{
  "id": "1910.13836",
  "version": "v1",
  "published": "2019-10-30T13:21:57.000Z",
  "updated": "2019-10-30T13:21:57.000Z",
  "title": "Erratum to \"The integer cohomology algebra of toric arrangements\"",
  "authors": [
    "Filippo Callegaro",
    "Emanuele Delucchi"
  ],
  "comment": "24 pages, 1 figure",
  "categories": [
    "math.AT",
    "math.CO"
  ],
  "abstract": "We point out two errors in the paper \"The integer cohomology algebra of toric arrangements, Advances in Mathematics, Vol. 313, pp.~746--802, 2017. The main error concerns Theorem 4.2.17. In particular the Diagram (8) does not commute in general. This invalidates the description for the ring structure of $H^*(M(\\mathcal{A});\\mathbb{Z})$ given in Theorem A and B. Still, under some restrictive hypotesis on $\\mathcal{A}$ the results of Theorem 4.2.17 holds. We show a workaround to provide a description of the cohomology ring $H^*(M(\\mathcal{A});\\mathbb{Z})$ when $\\mathcal{A}$ is a real complexified toric arrangement. The second error concerns the proof Theorem 7.2.1. The claim holds, but the proof is incorrect. We refer to a counterexample for the argument given in the proof and we provide references for a correct proof.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-30T13:21:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integer cohomology algebra",
      "main error concerns theorem",
      "second error concerns",
      "real complexified toric arrangement",
      "proof theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}