O número de Bruce-Roberts sobre uma ICIS - Lima-Pereira, Bárbara Karolline (2022)
In this work we study the relations between the Bruce-Roberts number, $μ_{BR}(f,X)$, the relative Bruce-Roberts, $μ_{BR}^{-}(f,X)$, of a function germ $f\in\mathcal{O}_{n}$ over an ICIS, $(X,0)\subset (\C^{n},0)$, and the Milnor numbers, $μ(f)$ and $μ(f^{-1}(0)\cap X,0)$. When $(X,0)$ is an isolated hypersurface singularity we show that $$μ_{BR}(f,X)=μ(f)+μ(f^{-1}(0)\cap X,0)+μ(X,0)-τ(X,0),$$ in which $τ(X,0)$ 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 $$μ_{BR}^{-}(f,X)=μ(f^{-1}(0)\cap X,0)+μ(X,0)-τ(X,0),$$ and that the relative logarithmic characteristic variety is Cohen-Macaulay, generalizing results of Bruce and Roberts (1988).