The structure of strata 𝜇=𝑐𝑜𝑛𝑠𝑡 in a critical set of a complete intersection singularity

1983 ◽  
pp. 663-665
Author(s):  
Yosef Yomdin
Keyword(s):  
Complete Intersection ◽  
Critical Set ◽  
Intersection Singularity ◽  
Complete Intersection Singularity

$4d$ $\mathcal{N} = 2$ SCFT from complete intersection singularity

2017 ◽  
Vol 21 (3) ◽  
pp. 801-855 ◽  
Author(s):  
Yifan Wang ◽  
Dan Xie ◽  
Stephen S.-T. Yau ◽  
Shing-Tung Yau
Keyword(s):  
Complete Intersection ◽  
Intersection Singularity ◽  
Complete Intersection Singularity

scholarly journals The Bruce–Roberts Number of A Function on A Hypersurface with Isolated Singularity

2020 ◽  
Vol 71 (3) ◽  
pp. 1049-1063
Author(s):  
J J Nuño-Ballesteros ◽  
B Oréfice-Okamoto ◽  
B K Lima-Pereira ◽  
J N Tomazella
Keyword(s):  
Complete Intersection ◽  
Hypersurface Singularity ◽  
Isolated Singularity ◽  
Characteristic Variety ◽  
Intersection Singularity ◽  
Complete Intersection Singularity ◽  
Isolated Complete Intersection Singularity

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.

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