{"paper":{"title":"The Bruce-Roberts number of a function on a hypersurface with isolated singularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"B\\'arbara K. L. Pereira, Bruna Or\\'efice-Okamoto, Jo\\~ao N. Tomazella, Juan J. Nu\\~no-Ballesteros","submitted_at":"2019-07-04T12:53:21Z","abstract_excerpt":"Let $(X,0)$ be an isolated hypersurface singularity defined by $\\phi\\colon(\\mathbb C^n,0)\\to(\\mathbb C,0)$ and $f\\colon(\\mathbb C^n,0)\\to\\mathbb C$ such that the Bruce-Roberts number $\\mu_{BR}(f,X)$ is finite. We first prove that $\\mu_{BR}(f,X)=\\mu(f)+\\mu(\\phi,f)+\\mu(X,0)-\\tau(X,0)$, where $\\mu$ and $\\tau$ are the Milnor and Tjurina numbers respectively of a function or an isolated complete intersection singularity. Second, we show that the logarithmic characteristic variety $LC(X,0)$ is Cohen-Macaulay. Both theorems generalize the results of a previous paper by some of the authors, in which t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02378","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"}