{"paper":{"title":"Uniform stable radius, L\\^e numbers and topological triviality for line singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christophe Eyral","submitted_at":"2017-04-27T08:37:39Z","abstract_excerpt":"Let $\\{f_t\\}$ be a family of complex polynomial functions with line singularities. We show that if $\\{f_t\\}$ has a uniform stable radius (for the corresponding Milnor fibrations), then the L\\^e numbers of the functions $f_t$ are independent of $t$ for all small $t$. In the case of isolated singularities --- a case for which the only non-zero L\\^e number coincides with the Milnor number --- a similar assertion was proved by M. Oka and D. O'Shea.\n  By combining our result with a theorem of J. Fern\\'andez de Bobadilla --- which says that families of line singularities in $\\mathbb{C}^n$, $n\\geq 5$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08475","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"}