{
  "id": "1805.01714",
  "version": "v1",
  "published": "2018-05-04T11:10:26.000Z",
  "updated": "2018-05-04T11:10:26.000Z",
  "title": "Intersection numbers of twisted cycles and cocycles for degenerate arrangements",
  "authors": [
    "Yoshiaki Goto"
  ],
  "comment": "32 pages",
  "categories": [
    "math.AG",
    "math.CA"
  ],
  "abstract": "We study the intersection numbers defined on twisted homology or cohomology groups that are associated with hypergeometric integrals corresponding to degenerate hyperplane arrangements in the projective $k$-space. We present formulas to evaluate the intersection numbers in the case when exactly one $(k+1)$-tuple of the hyperplanes intersects at a point. As an application, we discuss the contiguity relations of hypergeometric functions in terms of the intersection numbers on twisted cohomology groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-04T11:10:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C70",
      "32S22"
    ],
    "keywords": [
      "intersection numbers",
      "degenerate arrangements",
      "twisted cycles",
      "degenerate hyperplane arrangements",
      "twisted cohomology groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}