Real toric manifolds associated with chordal nestohedra
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910133420818432 |
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| author | Choi, Suyoung Yoon, Younghan |
| author_facet | Choi, Suyoung Yoon, Younghan |
| contents | This paper investigates the rational Betti numbers of real toric manifolds associated with chordal nestohedra. We consider the poset topology of a specific poset induced from a chordal building set, and show its EL-shellability. Based on this, we present an explicit description using alternating $\mathcal{B}$-permutations for a chordal building set $\mathcal{B}$, transforming the computing Betti numbers into a counting problem. This approach allows us to compute the $a$-number of a finite simple graph through permutation counting when the graph is chordal. In addition, we provide detailed computations for specific cases such as real Hochschild varieties corresponding to Hochschild polytopes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_11313 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Real toric manifolds associated with chordal nestohedra Choi, Suyoung Yoon, Younghan Algebraic Topology Algebraic Geometry Combinatorics 57S12, 14M25, 57N65, 05A05, 52B22 This paper investigates the rational Betti numbers of real toric manifolds associated with chordal nestohedra. We consider the poset topology of a specific poset induced from a chordal building set, and show its EL-shellability. Based on this, we present an explicit description using alternating $\mathcal{B}$-permutations for a chordal building set $\mathcal{B}$, transforming the computing Betti numbers into a counting problem. This approach allows us to compute the $a$-number of a finite simple graph through permutation counting when the graph is chordal. In addition, we provide detailed computations for specific cases such as real Hochschild varieties corresponding to Hochschild polytopes. |
| title | Real toric manifolds associated with chordal nestohedra |
| topic | Algebraic Topology Algebraic Geometry Combinatorics 57S12, 14M25, 57N65, 05A05, 52B22 |
| url | https://arxiv.org/abs/2407.11313 |