Proves μ_BR(f,X) = μ(f) + μ(φ,f) + μ(X,0) − τ(X,0) and that LC(X,0) is Cohen-Macaulay for isolated hypersurface singularities without assuming weighted homogeneity.
Mixed Bruce-Roberts numbers
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abstract
We extend the notion of $\mu^*$-sequence and Tjurina number of functions to the framework of Bruce-Roberts numbers, that is, to pairs formed by the germ at $0$ of a complex analytic variety $X\subseteq \mathbb C^n$ and a finitely $\mathcal R(X)$-determined analytic function germ $f:(\mathbb C^n,0)\to (\mathbb C,0)$. We analyze some fundamental properties of these numbers.
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2019 1verdicts
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The Bruce-Roberts number of a function on a hypersurface with isolated singularity
Proves μ_BR(f,X) = μ(f) + μ(φ,f) + μ(X,0) − τ(X,0) and that LC(X,0) is Cohen-Macaulay for isolated hypersurface singularities without assuming weighted homogeneity.