7 papers
Stability of closed leaves holomorphic foliations via torsion behavior of groups of germs
Javier Ribón
Consider a compact leaf of a holomorphic foliation such that all the leaves of the restriction of to some neighborhood of $\mathcal{L}…
Completely Integrable Foliations: Singular Locus, Invariant Curves and Topological Counterparts
Javier Ribón
We study codimension holomorphic foliations defined in a neighborhood of a point of a complex manifold that are completely integrable, i.e. with independent mero…
Constructive solution of Zariski's Moduli Problem for Plane Branches
Pedro Fortuny Ayuso, Javier Ribón
In this paper we give an explicit solution to Zariski's moduli problem for plane branches. We compute (in an algorithmic way) the set of Kähler differentials of an irreducible germ…
Explicit Computation of The Generic Component of the Analytic Moduli of a Plane Branch
Pedro Fortuny Ayuso, Javier Ribón
Let be a fixed equisingularity class of irreducible germs of complex analytic plane curves. We compute a basis of the -module of Kähler differentia…
Complexity of Puiseux solutions of differential and -difference equations of order and degree one
José Cano Torres, Pedro Fortuny Ayuso, Javier Ribón
We relate the complexity of both differential and -difference equations of order one and degree one and their solutions. Our point of view is to show that if the solutions are c…
The Poincaré problem for reducible curves
Pedro Fortuny Ayuso, Javier Ribón
We provide sharp lower bounds for the multiplicity of a local holomorphic foliation defined in a complex surface in terms of data associated to a germ of invariant curve. Then we a…
Nondegenerate germs of holomorphic foliations with prescribed holonomy
Javier Ribón, Rudy Rosas
We are interested in characterizing the holonomy maps associated to integral curves of non-degenerate singularities of holomorphic vector fields. Such a description is well-known i…