{"paper":{"title":"On conjectures of Itoh and of Lipman on the cohomology of normalized blow-ups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Manoj Kummini, Shreedevi K. Masuti","submitted_at":"2015-07-13T07:33:25Z","abstract_excerpt":"Let $(R, \\mathfrak{m}, \\Bbbk)$ be a Noetherian three-dimensional Cohen-Macaulay analytically unramified ring and $I$ an $\\mathfrak{m}$-primary $R$-ideal. Write $X = \\mathrm{Proj}\\left(\\oplus_{n \\in \\mathbb{N}} \\overline{I^n}t^n\\right)$. We prove some consequences of the vanishing of $\\mathrm{H}^2(X, \\mathscr{O}_X)$, whose length equals the the constant term $\\bar e_3(I)$ of the normal Hilbert polynomial of $I$. Firstly, $X$ is Cohen-Macaulay. Secondly, if the extended Rees ring $A := \\oplus_{n \\in \\mathbb{Z}} \\overline{I^n}t^n$ is not Cohen-Macaulay, and either $R$ is equicharacteristic or $\\o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03343","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"}