Classification of complex algebraic curves under blow-spherical equivalence

JE Sampaio, EC da Silva - Revista Matemática Complutense, 2024 - Springer
This article is devoted to studying complex algebraic sets under (global) blow-spherical
equivalence. This equivalence lives strictly between semialgebraic bi-Lipschitz equivalence …

On the Fukui–Kurdyka–Paunescu conjecture

A Fernandes, Z Jelonek, JE Sampaio - Compositio Mathematica, 2022 - cambridge.org
In this paper, we prove the Fukui–Kurdyka–Paunescu conjecture, which says that sub-
analytic arc-analytic bi-Lipschitz homeomorphisms preserve the multiplicities of real analytic …

A note on complex plane curve singularities up to diffeomorphism and their rigidity

A Fernández-Hernández… - Research in the …, 2024 - Springer
We prove that if two germs of plane curves (C, 0) and (C′, 0) with at least one singular
branch are equivalent by a (real) smooth diffeomorphism, then C is complex isomorphic to …

Classification of real algebraic curves under blow-spherical homeomorphisms at infinity

JE Sampaio, EC da Silva - São Paulo Journal of Mathematical Sciences, 2023 - Springer
Classification of real algebraic curves under blow-spherical homeomorphisms at infinity | São
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