7 papers
Lipschitz saturation of toric singularities in any dimension
François Bernard, Enrique Chávez-Martínez, Arturo E. Giles Flores
We describe the semigroup of the Lipschitz saturation of a complex analytic toric singularity in arbitrary dimension. We give a necessary and sufficient condition for a monomial in…
On the Lipschitz saturation of toric singularities
Daniel Duarte, Arturo E. Giles Flores
We begin the study of Lipschitz saturation for germs of toric singularities. By looking at their associated analytic algebras, we prove that if (X,0) is a germ of toric singularity…
On the fifth Whitney cone of a complex analytic curve
Arturo Giles Flores, Otoniel Nogueira da Silva, Jawad Snoussi
From a procedure to calculate the -cone of a reduced complex analytic curve at a singular point , we extract a collection of integers that we…
On tangency in equisingular families of curves and surfaces
Arturo Giles Flores, Otoniel Nogueira da Silva, Jawad Snoussi
We study the behavior of limits of tangents in topologically equivalent spaces. In the context of families of generically reduced curves, we introduce the -invariant of a curve…
On the Nash modification of a germ of complex analytic singularity
Arturo Giles Flores
For a germ of reduced, equidimensional complex analytic singularity its Nash modification can be constructed as an analytic subvariety $ Z \subset…
Local polar varieties in the geometric study of singularities
Arturo Giles Flores, Bernard Teissier
This text presents several aspects of the theory of equisingularity of complex analytic spaces from the standpoint of Whitney conditions. The goal is to describe from the geometric…
Specialization to the tangent cone and Whitney Equisingularity
Arturo Giles Flores
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 suffic…