相关论文: Symmetric Determinantal Singularities I: The Multi…
This paper is the second part of a two part paper which introduces the study of the Whitney Equisingularity of families of Symmetric determinantal singularities. This study reveals how to use the multiplicity of polar curves associated to a…
We study the topological triviality and the Whitney equisingularity of a family of isolated determinantal singularities. On one hand, we give a L\^e-Ramanujam type theorem for this kind of singularities by using the vanishing Euler…
We continue the development of the study of the equisingularity of isolated singularities, in the determinantal case. This version of the paper includes a substantial amount of new material (76% larger). The new material introduces the idea…
This paper addresses a very classical topic that goes back at least to Pl\"ucker: how to understand a plane curve singularity using its polar curves. Here, we explicitly construct the singular points of a plane curve singularity directly…
We study curve singularities in a smooth surface relative to a smooth boundary curve. We consider the semiuniversal deformations and equisingular deformations of curves with a fixed local intersection number $w$ with the boundary, and prove…
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 geometrical, topological, and algebraic viewpoints a canonical…
In this work we study equisingularity in a one-parameter flat family of generically reduced curves. We consider some equisingular criteria as topological triviality, Whitney equisingularity and strong simultaneous resolution. In this…
Using Newton polyhedra and non-degeneracy of matrices we present conditions which guarantee the Whitney equisingularity of families of isolated determinantal singularities.
We study equisingularity of families of reduced curves over smooth parameter spaces of arbitrary positive dimension, using the difference between two analytic invariants of a curve singularity: the multiplicity of its Jacobian ideal and its…
We give a description of the equisingularity of a family of normal surface singularities by numerical invariants belonging to them. By equisingularity we mean Whitney regularity or a more restrictive condition using the Nash modification.
We study a specific class of deformations of curve singularities: the case when the singular point splits to several ones, such that the total $\delta$ invariant is preserved. These are also known as equi-normalizable or equi-generic…
We prove a formula for the polar degree of projective hypersurfaces in terms of the Milnor data of the singularities, extending to 1-dimensional singularities the Dimca-Papadima result for isolated singularities. We discuss the…
We study codimension two determinantal varieties with isolated singularities. These singularities admit a unique smoothing, thus we can define their Milnor number as the middle Betti number of their generic fiber. For surfaces in C^4, we…
We present new results on equisingularity and equinormalizability of families with isolated non-normal singularities (INNS) of arbitrary dimension. We define a $\delta$-invariant and a $\mu$-invariant for an INNS and prove necessary and…
We study equisingular deformation problems for curves and surfaces in algebraic families, with particular emphasis on situations where nodal behavior is no longer generic. Extending classical Severi theory, we develop deformation--theoretic…
In this article we apply the results in the article "On Isolated Real Singularities I" to the study of real $ADE$-singularities. We show that said results enables us to find the homology groups of the Milnor fibres of real…
We give a $\delta$-constant criterion for equinormalizability of deformations of isolated (not necessarily reduced) curve singularities over smooth base spaces of dimension $\geq 1$. For one-parametric families of isolated curve…
Singularities of even smooth functions are studied. A classification of singular points which appear in typical parametric families of even functions with at most five parameters is given. Bifurcations of singular points near a caustic…
We study the behavior of limits of tangents in topologically equivalent spaces. In the context of families of generically reduced curves, we introduce the $s$-invariant of a curve and we show that in a Whitney equisingular family with the…
We explore some equisingularity criteria in one parameter families of generically reduced curves. We prove the equivalence between Whitney regularity and Zariski's discriminant criterion. We prove that topological triviality implies…