{"paper":{"title":"The toric ring of one dimensional simplicial complexes","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Antonino Ficarra, Dumitru I. Stamate, J\\\"urgen Herzog","submitted_at":"2023-06-08T08:16:29Z","abstract_excerpt":"Let $\\Delta$ be a 1-dimensional simplicial complex. Then $\\Delta$ may be identified with a finite simple graph $G$. In this article, we investigate the toric ring $R_G$ of $G$. All graphs $G$ such that $R_G$ is a normal domain are classified. For such a graph, we determine the set $\\mathcal{P}_G$ of height one monomial prime ideals of $R_G$. In the bipartite case, and in the case of whiskered cycles, this set is explicitly described. As a consequence, we determine the canonical class $[\\omega_{R_G}]$ and characterize the Gorenstein property of $R_G$. For a bipartite graph $G$, we show that $R_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.05020","kind":"arxiv","version":1},"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/2306.05020/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"}