Local geometry of analytic planar morphisms

Abstract

This work focuses in the study of local geometry of analytic planar morphisms. First, we introduce the basic concepts that will be needed to present the main part of the work. Secondly, we study the effect of analytic morphisms on plane curve singularites via direct and inverse images in terms of its jacobian, trunk and tangent map. We also present a new interpretation of the tangent map of a morphism. Finally, an open problem about the jacobian is introduced and we present an approach to a solution of a particular case of this problem.