Invariantes de germes de aplicações

• Ano de defesa: 2017
• Autor(a) principal: Ament, Daiane Alice Henrique
• Orientador(a): Tomazella, João Nivaldo
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de São Carlos; Câmpus São Carlos
• Programa de Pós-Graduação: Programa de Pós-Graduação em Matemática - PPGM
• Palavras-chave em Português: Obstrução de Euler de uma função; Número de Milnor determinantal; Singularidade determinantal isolada; Número de Milnor da imagem; Curvas singulares
• Palavras-chave em Inglês: Euler obstruction of a function; Determinantal Milnor number; Isolated determinantal singularity; Image Milnor number; Curve singularities
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufscar.br/handle/ufscar/8976

In this work, we show relations between invariants of map germs. First, we consider an analytic function germ f : (X, 0) —(C, 0) on an isolated determinantal singularity and we present a relation between the Euler obstruction of f and the determinantal Milnor number of f. In the particular case where (X, 0) is an isolated complete intersection singularity, we obtain a simple way to calculate the Euler obstruction of f as the difference between the dimension of two algebras. After, we work with map germs f : (X, 0) —— (C2, 0), where (X, 0) is a plane curve with isolated singularity. We introduce the image Milnor number to these map germs and we present a positive answer to the Mond’s conjecture in this context. The Mond’s conjecture proposes an inequality between two other invariants, the A^-codimension and the image Milnor number, in the case of map germs f : (Cn, 0) —(Cn+1, 0) when the dimensions (n,n + 1) is in Mather’s nice dimensions. The conjecture is true for n = 1, 2, and for the cases n > 3 is an open problem.