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arxiv: 1810.10570 · v1 · pith:EJ53QCKWnew · submitted 2018-10-24 · 🧮 math.AG · math.CV

Mixed Bruce-Roberts numbers

Carles Bivi\`a-Ausina , Mar\'ia Aparecida Soares Ruas This is my paper
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keywords mathbbnumbersanalyticbruce-robertsgermanalyzecomplexdetermined
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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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  1. The Bruce-Roberts number of a function on a hypersurface with isolated singularity

    math.AG 2019-07 unverdicted novelty 6.0

    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.