O número de Bruce-Roberts sobre uma ICIS
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...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | Brasil |
| Institución: | Universidade Federal de São Carlos (UFSCAR) |
| Repositorio: | Repositório Institucional da UFSCAR |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.ufscar.br:20.500.14289/15639 |
| Acceso en línea: | https://repositorio.ufscar.br/handle/20.500.14289/15639 |
| Access Level: | acceso abierto |
| Palabra clave: | 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 |
| Sumario: | 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). |
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