{"paper":{"title":"Koszul Gorenstein algebras from Cohen-Macaulay simplicial complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Alessio D'Al\\`i, Lorenzo Venturello","submitted_at":"2021-06-09T13:05:18Z","abstract_excerpt":"We associate with every pure flag simplicial complex $\\Delta$ a standard graded Gorenstein $\\mathbb{F}$-algebra $R_{\\Delta}$ whose homological features are largely dictated by the combinatorics and topology of $\\Delta$. As our main result, we prove that the residue field $\\mathbb{F}$ has a $k$-step linear $R_{\\Delta}$-resolution if and only if $\\Delta$ satisfies Serre's condition $(S_k)$ over $\\mathbb{F}$, and that $R_{\\Delta}$ is Koszul if and only if $\\Delta$ is Cohen-Macaulay over $\\mathbb{F}$. Moreover, we show that $R_{\\Delta}$ has a quadratic Gr\\\"{o}bner basis if and only if $\\Delta$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.05051","kind":"arxiv","version":2},"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/2106.05051/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"}