scholarly journals An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity

2008 ◽  
Vol 58 (5) ◽  
pp. 1761-1783 ◽  
Author(s):  
H.-Ch. Bothmer ◽  
Wolfgang Ebeling ◽  
Xavier Gómez-Mont
Keyword(s):  
Vector Field ◽  
Complete Intersection ◽  
Intersection Singularity ◽  
Algebraic Formula ◽  
Complete Intersection Singularity ◽  
Isolated 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.

$4d$ $\mathcal{N} = 2$ 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 A formula for the Euler characteristic of line singularities on singular spaces

2000 ◽  
Vol 61 (2) ◽  
pp. 335-343
Author(s):  
Guangfeng Jiang
Keyword(s):  
Complete Intersection ◽  
Euler Characteristic ◽  
Smooth Curve ◽  
Isolated Singularity ◽  
Singular Spaces ◽  
Critical Locus ◽  
Algebraic Formula ◽  
Line Singularities

We prove an algebraic formula for the Euler characteristic of the Milnor fibres of functions with critical locus a smooth curve on a space which is a weighted homogeneous complete intersection with isolated singularity.

Sign in / Sign up

Export Citation Format

Share Document