Herzog, Jürgen and Moradi, Somayeh and Topaçoğlu, Ayesha Asloob (2025) Toric rings attached to simplicial complexes. Collectanea Mathematica . ISSN 0010-0757 (Print) 2038-4815 (Online) Published Online First https://dx.doi.org/10.1007/s13348-025-00493-9
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Official URL: https://dx.doi.org/10.1007/s13348-025-00493-9
Abstract
We consider standard graded toric rings whose generators correspond to the faces of a simplicial complex. When is normal, it is shown that its divisor class group is free. For a flag complex which is the clique complex of a perfect graph, a nice description for the class group and the canonical module of in terms of the minimal vertex covers of the graph is given. Moreover, for a quasi-forest simplicial complex a quadratic Gröbner basis for the defining ideal of is presented. Using this fact we give combinatorial descriptions for the a-invariant and the Gorenstein property of.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Canonical module; Normal rings; Quasi-forests; Toric rings |
| Divisions: | Faculty of Engineering and Natural Sciences |
| Depositing User: | Ayesha Asloob Topaçoğlu |
| Date Deposited: | 22 Dec 2025 15:20 |
| Last Modified: | 22 Dec 2025 15:20 |
| URI: | https://research.sabanciuniv.edu/id/eprint/52982 |
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