{
  "id": "2407.16070",
  "version": "v1",
  "published": "2024-07-22T22:06:09.000Z",
  "updated": "2024-07-22T22:06:09.000Z",
  "title": "Homotopy Types Of Toric Orbifolds From Weyl Polytopes",
  "authors": [
    "Tao Gong"
  ],
  "categories": [
    "math.AT",
    "math.AG"
  ],
  "abstract": "Given a reduced crystallographic root system with a fixed simple system, it is associated to a Weyl group $W$, parabolic subgroups $W_K$'s and a polytope $P$ which is the convex hull of a dominant weight. The quotient $P/W_K$ can be identified with a polytope. Polytopes $P$ and $P/W_K$ are associated to toric varieties $X_P$ and $X_{P/W_K}$ respectively. It turns out the underlying topological spaces $X_P/W_K$ and $X_{P/W_K}$ are homotopy equivalent, when considering the polytopes in the real span of the root lattice or of the weight lattice.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-22T22:06:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "toric orbifolds",
      "homotopy types",
      "weyl polytopes",
      "reduced crystallographic root system",
      "root lattice"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}