{
  "id": "2106.12756",
  "version": "v1",
  "published": "2021-06-24T03:41:18.000Z",
  "updated": "2021-06-24T03:41:18.000Z",
  "title": "Roots of the characteristic polynomials of hyperplane arrangements and their restrictions and localizations",
  "authors": [
    "Takuro Abe"
  ],
  "comment": "18 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Terao's factorization theorem shows that if an arrangement is free, then its characteristic polynomial factors into the product of linear polynomials over the integer ring. This is not a necessary condition, but there are not so many non-free arrangements whose characteristic polynomial factors over the integer ring. On the other hand, the localization of a free arrangement is free, and its restriction is in many cases free, thus its characteristic polynomial factors. In this paper, we consider how their integer, or real roots behave.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-24T03:41:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S22"
    ],
    "keywords": [
      "characteristic polynomial factors",
      "hyperplane arrangements",
      "restriction",
      "localization",
      "real roots behave"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}