Sortable simplicial complexes and their associated toric rings
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913610725326848 |
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| author | Ficarra, Antonino Moradi, Somayeh |
| author_facet | Ficarra, Antonino Moradi, Somayeh |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10113 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sortable simplicial complexes and their associated toric rings Ficarra, Antonino Moradi, Somayeh Commutative Algebra 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. |
| title | Sortable simplicial complexes and their associated toric rings |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2412.10113 |