Curvas planas : fórmula de Noether e resolução de singularidades - Priscila Costa Ferreira de Jesus Bemm (2016)
The aim of this work is to demonstrate Noether's Formula, which allows us to evaluate the intersection index between two algebraic plane curves. For that, we consider the ring of formal power series and, through Weierstrass' Preparation Theorem, we realized it is possible to associate any series to a Weierstrass polynomial. After that, we consider every series as a Weierstrass' polynomial. For Noether's Formula it was necessary to present several results, among them the technique of resolution of singularities known as Blowing-up, Newton-Puiseux's Theorem and Newton's Implicit Function Theorem