{"paper":{"title":"H\\\"older equivalence of complex analytic curve singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Alexandre Fernandes, J. Edson Sampaio, Joserlan P. Silva","submitted_at":"2017-04-03T18:34:33Z","abstract_excerpt":"We prove that if two germs of irreducible complex analytic curves at $0\\in\\mathbb{C}^2$ have different sequence of characteristic exponents, then there exists $0<\\alpha<1$ such that those germs are not $\\alpha$-H\\\"older homeomorphic. For germs of complex analytic plane curves with several irreducible components we prove that if any two of them are $\\alpha$-H\\\"older homeomorphic, for all $0<\\alpha<1$, then there is a correspondence between their branches preserving sequence of characteristic exponents and intersection multiplicity of pair of branches. In particular, we recovery the sequence of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00755","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"}