The characterization of $(n-1)$-spheres with $n+4$ vertices having maximal Buchstaber number
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| Format: | Preprint |
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2023
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| _version_ | 1866915682258518016 |
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| author | Choi, Suyoung Jang, Hyeontae Vallée, Mathieu |
| author_facet | Choi, Suyoung Jang, Hyeontae Vallée, Mathieu |
| contents | We present a computationally efficient algorithm that is suitable for graphic processing unit implementation. This algorithm enables the identification of all weak pseudo-manifolds that meet specific facet conditions, drawn from a given input set. We employ this approach to enumerate toric colorable seeds. Consequently, we achieve a comprehensive characterization of $(n-1)$-dimensional PL spheres with $n+4$ vertices that possess a maximal Buchstaber number.
A primary focus of this research is the fundamental categorization of non-singular complete toric varieties of Picard number $4$. This classification serves as a valuable tool for addressing questions related to toric manifolds of Picard number $4$. Notably, we have determined which of these manifolds satisfy equality within an inequality regarding the number of minimal components in their rational curve space. This addresses a question posed by Chen, Fu, and Hwang in 2014 for this specific case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2301_00806 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The characterization of $(n-1)$-spheres with $n+4$ vertices having maximal Buchstaber number Choi, Suyoung Jang, Hyeontae Vallée, Mathieu Geometric Topology Computational Geometry Distributed, Parallel, and Cluster Computing 57S12 (primary), 14N10 (secondary), 14M25 We present a computationally efficient algorithm that is suitable for graphic processing unit implementation. This algorithm enables the identification of all weak pseudo-manifolds that meet specific facet conditions, drawn from a given input set. We employ this approach to enumerate toric colorable seeds. Consequently, we achieve a comprehensive characterization of $(n-1)$-dimensional PL spheres with $n+4$ vertices that possess a maximal Buchstaber number. A primary focus of this research is the fundamental categorization of non-singular complete toric varieties of Picard number $4$. This classification serves as a valuable tool for addressing questions related to toric manifolds of Picard number $4$. Notably, we have determined which of these manifolds satisfy equality within an inequality regarding the number of minimal components in their rational curve space. This addresses a question posed by Chen, Fu, and Hwang in 2014 for this specific case. |
| title | The characterization of $(n-1)$-spheres with $n+4$ vertices having maximal Buchstaber number |
| topic | Geometric Topology Computational Geometry Distributed, Parallel, and Cluster Computing 57S12 (primary), 14N10 (secondary), 14M25 |
| url | https://arxiv.org/abs/2301.00806 |