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- Title
The Bruce–Roberts Number of A Function on A Hypersurface with Isolated Singularity.
- Authors
Nuño-Ballesteros, J J; Oréfice-Okamoto, B; Lima-Pereira, B K; Tomazella, J N
- Abstract
Let |$(X,0)$| be an isolated hypersurface singularity defined by |$\phi \colon ({\mathbb{C}}^n,0)\to ({\mathbb{C}},0)$| and |$f\colon ({\mathbb{C}}^n,0)\to{\mathbb{C}}$| such that the Bruce–Roberts number |$\mu _{BR}(f,X)$| is finite. We first prove that |$\mu _{BR}(f,X)=\mu (f)+\mu (\phi ,f)+\mu (X,0)-\tau (X,0)$| , where |$\mu $| and |$\tau $| are the Milnor and Tjurina numbers respectively of a function or an isolated complete intersection singularity. Second, we show that the logarithmic characteristic variety |$LC(X,0)$| is Cohen–Macaulay. Both theorems generalize the results of a previous paper by some of the authors, in which the hypersurface |$(X,0)$| was assumed to be weighted homogeneous.
- Subjects
AUTHORS; FINITE, The
- Publication
Quarterly Journal of Mathematics, 2020, Vol 71, Issue 3, p1049
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmathj/haaa015