{"paper":{"title":"Equimultiplicity of topologically equisingular families of parametrized surfaces in $\\mathbb C^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Maria Aparecida Soares Ruas","submitted_at":"2013-02-23T13:57:55Z","abstract_excerpt":"We provide a positive answer to Zariski's conjecture for families of singular surfaces in $\\mathbb C^3,$ under the condition that the family has a smooth normalisation. As a corollary of the result, we obtain a surprising characterization of the Whitney equisingularity of one parameter families of $\\mathcal A$ finitely determined map-germs $f_t: (\\mathbb C^2,0) \\to (\\mathbb C^3,0),$ in terms of the constancy of only one invariant, the Milnor number of the double point locus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5800","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"}