Aritmética de los semigrupos de Arf y saturados. Aplicaciones.
Arrangements of lines and monodromy of plane curves
Base points of polar curves
The base points of the system of polar curves of an irreducible algebroid plane curve with general moduli are determined. As consequences a lower bound for the Tjurina number and many continuous analytic invariants of the curve are found.
Bernstein classes
One of the classical Bernstein inequalities compares the maxima of a polynomial of a given degree on the interval [-1,1] and on the ellipse in the complex plane with the focuses -1, 1 and the semiaxes . We prove a similar inequality for a branch of an algebraic function of a given degree on the maximal disk of its regularity, with the explicitly given constant, depending on the degree only. In particular, this improves a recent inequality of Fefferman and Narasimhan and answers one of their questions....
Calcolo del conduttore di curve algebriche e ideali di punti
Chains on the Eggers tree and polar curves.
Characterization of jacobian Newton polygons of plane branches and new criteria of irreducibility
In this paper we characterize, in two different ways, the Newton polygons which are jacobian Newton polygons of a plane branch. These characterizations give in particular combinatorial criteria of irreducibility for complex series in two variables and necessary conditions which a complex curve has to satisfy in order to be the discriminant of a complex plane branch.
Characterization of non-degenerate plane curve singularities.
Characterization of the Hilbert-Samuel polynomials of curve singularities
Cohen-Macaulay module type
Cohomology of moduli spaces of stable curves.
Combinations of rational singularities on plane sextic curves with the sum of Milnor numbers less than sixteen
Compactification of the space of vector bundles on a singular curve.
Compactified Jocobian of some unibranch curves.
Computing limit linear series with infinitesimal methods
Alexander and Hirschowitz determined the Hilbert function of a generic union of fat points in a projective space when the number of fat points is much bigger than the greatest multiplicity of the fat points. Their method is based on a lemma which determines the limit of a linear system depending on fat points approaching a divisor.Other Hilbert functions were computed previously by Nagata. In connection with his counter-example to Hilbert’s fourteenth problem, Nagata determined the Hilbert function...
Construcción canónica de cuspides y aproximación a su jacobiana.
Correction to the gonality of smooth curves with plane models.
Cotangent Functors of Curve Singularities.
Courbes de semi-groupe donné.
Courbes lisses qui ne sont pas intersection de 3 surfaces dans l'espace projectif