O número de Bruce-Roberts sobre uma ICIS

• Autor(a) principal: Lima-Pereira, Bárbara Karolline
• Data de Publicação: 2022
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da UFSCAR
• Texto Completo: https://repositorio.ufscar.br/handle/ufscar/15639
• topic: Interseção completa com singularidade isolada; Número de Bruce-Roberts; Variedade logarítmica característica; Isolated complete intersection singularity; The Bruce-Roberts number; Logarithmic characteristic variety; CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA::TEORIA DAS SINGULARIDADES E TEORIA DAS CATASTROFES

In this work we study the relations between the Bruce-Roberts number, $\mu_{BR}(f,X)$, the relative Bruce-Roberts, $\mu_{BR}^{-}(f,X)$, of a function germ $f\in\mathcal{O}_{n}$ over an ICIS, $(X,0)\subset (\C^{n},0)$, and the Milnor numbers, $\mu(f)$ and $\mu(f^{-1}(0)\cap X,0)$. When $(X,0)$ is an isolated hypersurface singularity we show that $$\mu_{BR}(f,X)=\mu(f)+\mu(f^{-1}(0)\cap X,0)+\mu(X,0)-\tau(X,0),$$ in which $\tau(X,0)$ is the Tjurina number, and that the logarithmic characteristic variety is Cohen-Macaulay, generalizing results of Oréfice-Okamoto's Thesis. When $(X,0)$ is an ICIS we show that $$\mu_{BR}^{-}(f,X)=\mu(f^{-1}(0)\cap X,0)+\mu(X,0)-\tau(X,0),$$ and that the relative logarithmic characteristic variety is Cohen-Macaulay, generalizing results of Bruce and Roberts (1988).