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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.10113 |
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Table of Contents:
- Let $Γ$ be a $d$-flag sortable simplicial complex. We consider the toric ring $R_Γ=K[{\bf x}_Ft:F\in Γ]$ and the Rees algebra of the facet ideals $I(Γ^{[i]})$ of pure skeletons of $Γ$. We show that these algebras are Koszul, normal Cohen-Macaulay domains. Moreover, we study the Gorenstein property, the canonical module, and the $a$-invariant of the normal domain $R_Γ$ by investigating its divisor class group. Finally, it is shown that any $d$-flag sortable simplicial complex is vertex decomposable, which provides a characterization of the Cohen-Macaulay property of such complexes.