{"paper":{"title":"Local Bezout estimates and multiplicities of parameter and primary ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Eduard Boda, Peter Schenzel","submitted_at":"2017-02-13T10:20:50Z","abstract_excerpt":"Let $\\mathfrak{q}$ denote an $\\mathfrak{m}$-primary ideal of a $d$-dimensional local ring $(A, \\mathfrak{m}).$ Let $\\underline{a} = a_1,\\ldots,a_d \\subset \\mathfrak{q}$ be a system of parameters. Then there is the following inequality for the multiplicities $c \\cdot e(\\mathfrak{q};A) \\leq e(\\underline{a};A)$ where $c$ denotes the product of the initial degrees of $a_i$ in the form ring $G_A(\\mathfrak{q}).$ The aim of the paper is a characterization of the equality as well as a description of the difference by various homological methods via Koszul homology. To this end we have to characterize "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03704","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"}