5 papers
On the analytic equivalence of branches in (n+1)-space
Marcelo Escudeiro Hernandes, Welinton Anderson Rocha, Maria Elenice Rodrigues Hernandes
In this paper, we consider Newton-Puiseux parametrizations of irreducible curves in (n+1)-space, n greater or equal to 1, within a fixed semigroup under the action of Mather's grou…
Bernstein polynomial and value set of differentials for plane branches
Andrea Gomes Guimarães, Marcelo Escudeiro Hernandes
In this work, we study the relation between the roots of the Bernstein polynomial and the value set of differentials for plane branches. For plane branches def…
On the Saito basis for plane curves
Emilio de Carvalho, Percy Fernández-Sánchez, Marcelo Escudeiro Hernandes
We present some results concerning the Saito module and the torsion submodule of an analytic plane curve, and we provide a method for computing them. Using this algorithm, we compu…
The Tjurina number of a plane curve with two branches and high intersection multiplicity
Patricio Almirón, Marcelo E. Hernandes
In this paper we provide a family of reduced plane curves with two branches that have a constant Tjurina number in their equisingularity class, along with a closed formula for it i…
On the Zariski invariant of plane branches
Marcelo Escudeiro Hernandes, Mauro Fernando Hernández Iglesias
We show how to obtain the Zariski invariant of a plane branch employing the contact order or the intersection multiplicity with elements in a particular family of curves and we pre…