{"paper":{"title":"The Chern coefficients of local rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Wolmer V. Vasconcelos","submitted_at":"2008-02-01T21:14:49Z","abstract_excerpt":"The Chern numbers of the title are the first coefficients (after the multiplicities) of the Hilbert functions of various filtrations of ideals of a local ring $(R, \\mathfrak{m})$. For a Noetherian (good) filtration $\\mathcal{A}$ of $\\mathfrak{m}$-primary ideals, the positivity and bounds for $e_1(\\mathcal{A})$ are well-studied if $R$ is Cohen-Macaulay, or more broadly, if $R$ is a Buchsbaum ring or mild generalizations thereof.\n  For arbitrary geometric local domains, we introduce techniques based on the theory of maximal Cohen-Macaulay modules and of extended multiplicity functions to establi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.0205","kind":"arxiv","version":2},"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"}