{"paper":{"title":"Stability of Depth and Cohen-Macaulayness of Integral Closures of Powers of Monomial Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Le Tuan Hoa, Tran Nam Trung","submitted_at":"2017-06-23T09:05:48Z","abstract_excerpt":"Let $I$ be a monomial ideal $I$ in a polynomial ring $R = k[x_1,...,x_r]$. In this paper we give an upper bound on $\\overline{\\dstab} (I)$ in terms of $r$ and the maximal generating degree $d(I)$ of $I$ such that $\\depth R/\\overline{I^n}$ is constant for all $n\\geqslant \\overline{\\dstab}(I)$. As an application, we classify the class of monomial ideals $I$ such that $\\overline{I^n}$ is Cohen-Macaulay for some integer $n\\gg 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07603","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":""},"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"}