{"paper":{"title":"On the structure of sequentially Cohen--Macaulay bigraded modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ahad Rahimi, Leila Parsaei Majd","submitted_at":"2013-01-29T07:22:31Z","abstract_excerpt":"Let $K$ be a field and $S=K[x_1,\\ldots,x_m, y_1,\\ldots,y_n]$ be the standard bigraded polynomial ring over $K$. In this paper, we explicitly describe the structure of finitely generated bigraded \"sequentially Cohen--Macaulay\" $S$-modules with respect to $Q=(y_1,\\ldots,y_n)$. Next, we give a characterization of sequentially Cohen--Macaulay modules with respect to $Q$ in terms of local cohomology modules. Cohen--Macaulay modules that are sequentially Cohen--Macaulay with respect to $Q$ are considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6846","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":""},"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"}