{
  "id": "2206.15059",
  "version": "v1",
  "published": "2022-06-30T06:42:53.000Z",
  "updated": "2022-06-30T06:42:53.000Z",
  "title": "Generalization of the addition and restriction theorems from free arrangements to the class of projective dimension one",
  "authors": [
    "Takuro Abe"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study a generalized version of Terao's famous addition theorem for free arrangements to the category of those with projective dimension one. Namely, we give a criterion to determine the algebraic structure of logarithmic derivation modules of the addition when the deletion and restrictions are free with a mild condition. Also, we introduce a class of divisionally SPOG arrangements whose SPOGness depends only on the intersection lattice like Terao's famous conjecture on combinatoriality of freeness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-30T06:42:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S22"
    ],
    "keywords": [
      "free arrangements",
      "projective dimension",
      "restriction theorems",
      "generalization",
      "teraos famous addition theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}