{
  "id": "2003.13553",
  "version": "v1",
  "published": "2020-03-30T15:28:12.000Z",
  "updated": "2020-03-30T15:28:12.000Z",
  "title": "Bordifications of hyperplane arrangements and their curve complexes",
  "authors": [
    "Michael W. Davis",
    "Jingyin Huang"
  ],
  "comment": "62 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "The complement of an arrangement of hyperplanes in $\\mathbb C^n$ has a natural bordification to a manifold with corners formed by removing (or \"blowing up\") tubular neighborhoods of the hyperplanes and certain of their intersections. When the arrangement is the complexification of a real simplicial arrangement, the bordification closely resembles Harvey's bordification of moduli space. We prove that the faces of the universal cover of the bordification are parameterized by the simplices of a simplicial complex $\\mathcal{C}$, the vertices of which are the irreducible \"parabolic subgroups\" of the fundamental group of the arrangement complement. So, the complex $\\mathcal{C}$ plays a similar role for an arrangement complement as the curve complex does for moduli space. Also, in analogy with curve complexes and with spherical buildings, we prove that $\\mathcal{C}$ has the homotopy type of a wedge of spheres.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-30T15:28:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "curve complex",
      "hyperplane arrangements",
      "bordification closely resembles harveys bordification",
      "moduli space",
      "arrangement complement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 62,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}