{"paper":{"title":"Toric rings attached to simplicial complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Ayesha Asloob Qureshi, J\\\"urgen Herzog, Somayeh Moradi","submitted_at":"2023-02-07T18:09:32Z","abstract_excerpt":"We consider standard graded toric rings $R_{\\Delta}$ whose generators correspond to the faces of a simplicial complex $\\Delta$. When $R_{\\Delta}$ is normal, it is shown that its divisor class group is free. For a flag complex $\\Delta$ which is the clique complex of a perfect graph, a nice description for the class group and the canonical module of $R_{\\Delta}$ in terms of the minimal vertex covers of the graph is given. Moreover, for a quasi-forest simplicial complex a quadratic Gr\\\"obner basis for the defining ideal of $R_{\\Delta}$ is presented. Using this fact we give combinatorial descripti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.03653","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.03653/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}