On the connection between coordinate and diagonal arrangement complements
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910130406162432 |
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| author | Tril, Vsevolod |
| author_facet | Tril, Vsevolod |
| contents | We study diagonal arrangement complements $D(K)$ in $\mathbb{C}^m$. We consider the class of simplicial complexes $K$ in which any two missing faces have a common vertex, and prove that the coordinate arrangement complement $U(K)$ is the double suspension of the diagonal arrangement complement $D(K)$. In the case of subspace arrangements in $\mathbb{R}^m$ the coordinate arrangement complement $U_{\mathbb{R}}(K)$ is the single suspension of $D_{\mathbb{R}}(K)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_18001 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the connection between coordinate and diagonal arrangement complements Tril, Vsevolod Algebraic Topology Combinatorics 13F55, 14N20, 55P10, 55P40, 57S12 We study diagonal arrangement complements $D(K)$ in $\mathbb{C}^m$. We consider the class of simplicial complexes $K$ in which any two missing faces have a common vertex, and prove that the coordinate arrangement complement $U(K)$ is the double suspension of the diagonal arrangement complement $D(K)$. In the case of subspace arrangements in $\mathbb{R}^m$ the coordinate arrangement complement $U_{\mathbb{R}}(K)$ is the single suspension of $D_{\mathbb{R}}(K)$. |
| title | On the connection between coordinate and diagonal arrangement complements |
| topic | Algebraic Topology Combinatorics 13F55, 14N20, 55P10, 55P40, 57S12 |
| url | https://arxiv.org/abs/2409.18001 |