Raízes aproximadas características de uma curva plana

Abstract

The purpose of this work is to show that the minimal embedded resolution of a cha- racteristic approximate root of a plane branch is determined by the minimal embedded resolution of this branch. For that we study algebroid plane curves with their Newton-Puiseux parametrizations, the characteristics exponents, the intersection multiplicity of two curves, the semigroup of values of an algebroid plane curve, and the canonical resolution process of singularities. We conclude with the relations between a branch and its approximate roots. We define characteristic approximate roots and semiroots, and we show that the characteristic exponents of a semiroot of a curve can be determined by the characteristic exponents of the curve. We finish with the minimal embedded resolution process of a curve and its characteristic roots