Real toric manifolds associated with chordal nestohedra

Suyoung Choi; Younghan Yoon

doi:10.1016/j.jcta.2025.106102

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arXiv · 2407.11313

Real toric manifolds associated with chordal nestohedra

Suyoung Choi·Younghan Yoon

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Abstract

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.

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BibTeX RIS

Suyoung Choi, Younghan Yoon. 2024-07-16. Real toric manifolds associated with chordal nestohedra. https://doi.org/10.1016/j.jcta.2025.106102

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