{"paper":{"title":"Local Cohomology of Multi-Rees Algebras with Applications to Joint Reductions and Complete Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"J. K. Verma, Shreedevi K. Masuti, Tony J. Puthenpurakal","submitted_at":"2014-07-06T13:25:37Z","abstract_excerpt":"In this paper, we obtain a generalization, in dimension $3$, of a theorem of David Rees about joint reductions of the bigraded filtration $\\{ \\overline{I^rJ^s}\\}$ of complete ${\\mathfrak m}$-primary ideals and vanishing of the second normal Hilbert coefficient $\\overline{e}_2(IJ)$ where $R$ is a two-dimensional Cohen-Macaulay analytically unramified local ring with maximal ideal $\\mathfrak m.$ This generalization is obtained as a consequence of a formula for the third local cohomology module of the extended Rees algebras of the $\\mathbb Z^3$-graded filtration $\\{\\overline{I^rJ^sK^t}\\}$ with su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1493","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"}