{"paper":{"title":"Specialization to the tangent cone and Whitney Equisingularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Arturo Giles Flores","submitted_at":"2011-06-06T20:21:36Z","abstract_excerpt":"Let (X,0) be a reduced, equidimensional germ of analytic singularity with reduced tangent cone (C_{X,0},0). We prove that the absence of exceptional cones is a necessary and sufficient condition for the smooth part \\X^0 of the specialization to the tangent cone \\phi: \\X \\to \\C to satisfy Whitney's conditions along the parameter axis Y. This result is a first step in generalizing to higher dimensions L\\^e and Teissier's result for hypersurfaces of \\C^3 which establishes the Whitney equisingularity of X and its tangent cone under this conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1191","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"}