Singularidades de ecuaciones diferenciales y foliaciones

This project is centered into the study of the solutions of the equation defined by an integrable holomorphic differential one form in a neighbourhood of a singular point with special emphasis on the bidimensional case. The objective is the progress in the following topics: a) design of desingularization techniques based on classical constructions of algebraic geometry; b) computation of the analytic "moduli" associated to a fixed topological or formal type of the equation. Subsequently results on these subjects will be used in analyzing the global behaviour of holomorphic dynamical systems on the complex projective plane.