Browsing Singularity Theory and Algebraic Geometry by Author "Sampaio, J.E."
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Globally subanalytic CMC surfaces in $\mathbb{R}^3$ with singularities
Sampaio, J.E. (20200302)In this paper we present a classification of a class of globally subanalytic CMC surfaces in $\mathbb{R}^3$ that generalizes the recent classification made by Barbosa and do Carmo in 2016. We show that a globally subanalytic ... 
Hölder equivalence of complex analytic curve singularities
Fernandes, A.; Sampaio, J.E.; Silva, J.P. (20180806)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 ... 
Moderately Discontinuous Homology
Fernández de Bobadilla, J.; Heinze, S.; Sampaio, J.E. (20210101)We introduce a new metric homology theory, which we call Moderately Discontinuous Homology, designed to capture Lipschitz properties of metric singular subanalytic germs. The main novelty of our approach is to allow ... 
Multiplicity and degree as bi‐Lipschitz invariants for complex sets
Fernandes, A.; Fernández de Bobadilla, J.; Sampaio, J.E. (20180829)We study invariance of multiplicity of complex analytic germs and degree of complex affine sets under outer biLipschitz transformations (outer biLipschitz homeomorphims of germs in the first case and outer biLipschitz ... 
Multiplicity of singularities is not a biLipschitz invariant
Birbrair, L.; Fernandes, A.; Sampaio, J.E.; Verbitsky, M. (20200117)It was conjectured that multiplicity of a singularity is biLipschitz invariant. We disprove this conjecture constructing examples of biLipschitz equivalent complex algebraic singularities with different values of multiplicity. 
Multiplicity, regularity and blowspherical equivalence of complex analytic sets
Sampaio, J.E. (20200129)This paper is devoted to study multiplicity and regularity of complex analytic sets. We present an equivalence for complex analytical sets, named blowspherical equivalence and we obtain several applications with this new ... 
On Lipschitz rigidity of complex analytic sets
Fernandes, A.; Sampaio, J.E. (20190226)We prove that any complex analytic set in $\mathbb{C}^n$ which is Lipschitz normally embedded at infinity and has tangent cone at infinity that is a linear subspace of $\mathbb{C}^n$ must be an affine linear subspace of ... 
On Zariski’s multiplicity problem at infinity
Sampaio, J.E. (20180814)We address a metric version of Zariski's multiplicity conjecture at infinity that says that two complex algebraic affine sets which are biLipschitz homeomorphic at infinity must have the same degree. More specifically, ... 
A proof of the differentiable invariance of the multiplicity using spherical blowingup
Sampaio, J.E. (20180421)In this paper we use some properties of spherical blowingup to give an alternative and more geometric proof of GauLipman Theorem about the differentiable invariance of the multiplicity of complex analytic sets. Moreover, ... 
Semialgebraic CMC surfaces in $\mathbb{R}^3$ with singularities
Sampaio, J.E. (20180630)In this paper we present a classification of a class of semialgebraic CMC surfaces in $\mathbb{R}^3$ that generalizes the recent classification made by Barbosa and do Carmo in 2016 (complete reference is in the paper), we ... 
Some classes of homeomorphisms that preserve multiplicity and tangent cones
Sampaio, J.E. (20180819)In this paper it is presented some classes of homeomorphisms that preserve multiplicity and tangent cones of complex analytic sets. Moreover, we present a class of homeomorphisms that has the multiplicity as an invariant ... 
Some classes of homeomorphisms that preserve multiplicity and tangent cones
Sampaio, J.E. (20190528)In this paper we present some applications of A'CampoLê's Theorem and we study some relations between Zariski's Questions A and B. It is presented some classes of homeomorphisms that preserve multiplicity and tangent cones ... 
Some classes of homeomorphisms that preserve multiplicity and tangent cones
Sampaio, J.E. (20200101)In this paper we present some applications of A’CampoLˆe’s Theorem and we study some relations between Zariski’s Questions A and B. It is presented some classes of homeomorphisms that preserve multiplicity and tangent ...