超曲面上函数的相对Bruce-Roberts数
The relative Bruce-Roberts number of a function on a hypersurface
摘要：
本文研究孤立超曲面奇点$(X,0)$上函数的相对Bruce-Roberts数$μ_{BR}^{-}(f,X)$.我们表明，$μ_{BR}^{-}(f,X)$等于总和的Milnor数的纤维$μ(f^{-1}(0)\cap X,0)$加上差异$μ(X,0)-τ(X,0)$之间的Milnor和Tjurina数的$(X,0)$。作为应用，我们证明了通常的Bruce-Roberts数$μ_{BR}(f,X)$等于$μ(f)+μ_{BR}^{-}(f,X)$ .我们还推导出由对数特征簇$LC(X)$通过在周围空间中消去对应于$X$的补的分量而得到的相对对数特征簇$LC(X)^-$是Cohen-Macaulay。
英文摘要：
We consider the relative Bruce-Roberts number $μ_{BR}^{-}(f,X)$ of a function on an isolated hypersurface singularity $(X,0)$. We show that $μ_{BR}^{-}(f,X)$ is equal to the sum of the Milnor number of the fibre $μ(f^{-1}(0)\cap X,0)$ plus the difference $μ(X,0)-τ(X,0)$ between the Milnor and the Tjurina numbers of $(X,0)$. As an application, we show that the usual Bruce-Roberts number $μ_{BR}(f,X)$ is equal to $μ(f)+μ_{BR}^{-}(f,X)$. We also deduce that the relative logarithmic characteristic variety $LC(X)^-$, obtained from the logarithmic characteristic variety $LC(X)$ by eliminating the component corresponding to the complement of $X$ in the ambient space, is Cohen-Macaulay.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
