{"paper":{"title":"Local Cohomology of Bigraded Rees Algebras and Normal Hilbert Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"J. K. Verma, Shreedevi K. Masuti","submitted_at":"2013-07-12T12:20:36Z","abstract_excerpt":"Let $(R,\\m)$ be an analytically unramified Cohen-Macaulay local ring of dimension 2 with infinite residue field and $\\ov{I}$ be the integral closure of an ideal $I$ in $R$. Necessary and sufficient conditions are given for $\\ov{I^{r+1}J^{s+1}}=a\\ov{I^rJ^{s+1}}+b\\ov{I^{r+1}J^s}$ to hold ${for all}r \\geq r_0{and}s \\geq s_0$ in terms of vanishing of $[H^2_{(at_1,bt_2)}(\\ov{\\mathcal{R}^\\prime}(I,J))]_{(r_0,s_0)}$, where $a \\in I,b \\in J$ is a good joint reduction of the filtration $\\{\\ov{I^rJ^s}\\}.$ This is used to derive a theorem due to Rees on normal joint reduction number zero. The vanishing o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3431","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"}