It was shown by Henry and Parusiński in 2003 that the bi-Lipschitz right equivalence of function germs admits moduli. In this article, we introduce the notion of Lipschitz simple function germ and present the complete ...

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 ...

We survey the proof of the Nash conjecture for surfaces and show how geometric and topological ideas developed in previous articles by the authors influenced it. Later, we summarize the main ideas in the higher dimensional ...

This paper is devoted to study multiplicity and regularity of complex analytic sets. We present an equivalence for complex analytical sets, named blow-spherical equivalence and we obtain several applications with this new ...

It was conjectured that multiplicity of a singularity is bi-Lipschitz invariant. We disprove this conjecture constructing examples of bi-Lipschitz equivalent complex algebraic singularities with different values of multiplicity.

Given a reflection group G acting on a complex vector space V , a reflection map is the composition of an embedding X → V with the quotient map V → Cp of G. We show how these maps, which can highly singular, may be studied ...

We algorithmically compute the intersection cohomology Betti numbers of any complete normal algebraic variety with a torus action of complexity one.

We consider the possible disentanglements of holomorphic map germs f : (Cn, 0) → (CN , 0), 0 < n < N, with nonisolated locus of instability Inst(f). The aim is to achieve lower bounds for their (homological) connectiv- ity ...

Given a smooth, projective variety $X$ and an effective divisor $D\,\subseteq\, X$, it is well-known that the (topological) obstruction to the deformation of the fundamental class of $D$ as a Hodge class, lies in ...

We study the classification of plane curve singularities in arbitrary characteristic. We first give a bound for the determinacy of a plane curve singularity with respect to pararametrization equivalence in terms of its ...