Homotopy Types Of Toric Orbifolds From Weyl Polytopes
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917730855157760 |
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| author | Gong, Tao |
| author_facet | Gong, Tao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16070 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homotopy Types Of Toric Orbifolds From Weyl Polytopes Gong, Tao Algebraic Topology Algebraic Geometry 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. |
| title | Homotopy Types Of Toric Orbifolds From Weyl Polytopes |
| topic | Algebraic Topology Algebraic Geometry |
| url | https://arxiv.org/abs/2407.16070 |