Curvas planas : fórmula de Noether e resolução de singularidades

• Ano de defesa: 2016
• Autor(a) principal: Priscila Costa Ferreira de Jesus Bemm
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Brasil; Departamento de Matemática; Programa de Pós-Graduação em Matemática; UEM; Maringá, PR; Centro de Ciências Exatas
• Palavras-chave em Português: Fórmula de Noether, Blowing-up; Desingularização; Índice de interseção; Curvas planas (Geometria); Noether´s formula; Resolution of singularities; Plane curves; Ciências Exatas e da Terra; Matemática
• Link de acesso: http://repositorio.uem.br:8080/jspui/handle/1/5473

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