论文标题
Bruce-Roberts在ICIS上的功能数量
The Bruce-Roberts Numbers of a Function on an ICIS
论文作者
论文摘要
我们给出了布鲁斯·罗伯特人编号的公式$μ__{br}（f，x）$及其相对版本$μ__{br}^{ - } { - }（f，x）$相对于ICIS $（x，0）$。我们表明$μ_{br}^{ - }（f，x）=μ（f^{ - 1}（0）（0）\ cap x，0）+μ（x，0） - τ（x，0）$，其中$μ$和$μ$和$μ$和$τ$分别是ICIS的Milnor和Tjurina数字。 $μ_{br}（f，x）$的公式更为复杂，还涉及$μ（f）$，并且就理想$ i_x $和$ jf $而言。我们还考虑对数特性品种$ LC（x）$及其相对版本$ LC（x）^{ - } $。我们表明，$ LC（x）^{ - } $是Cohen-Macaulay，$ LC（x）$在任何时候都不是Cohen-Macaulay，niond note noce note noce note note not $ x \ times \ {0 \} $。当$（x，0）$具有编纂时，以及布鲁斯和罗伯茨的加权均匀时，我们会概括作者提出的先前结果。
We give formulas for the Bruce-Roberts number $μ_{BR}(f,X)$ and its relative version $μ_{BR}^{-}(f,X)$ of a function $f$ with respect to an ICIS $(X,0)$. We show that $μ_{BR}^{-}(f,X)=μ(f^{-1}(0)\cap X,0)+μ(X,0)-τ(X,0)$, where $μ$ and $τ$ are the Milnor and Tjurina numbers, respectively, of the ICIS. The formula for $μ_{BR}(f,X)$ is more complicated and also involves $μ(f)$ and some lengths in terms of the ideals $I_X$ and $Jf$. We also consider the logarithmic characteristic variety, $LC(X)$, and its relative version, $LC(X)^{-}$. We show that $LC(X)^{-}$ is Cohen-Macaulay and that $LC(X)$ is Cohen-Macaulay at any point not in $X\times\{0\}$. We generalize previous results presented by the authors when $(X,0)$ has codimension one and by Bruce and Roberts when it is weighted homogeneous of any codimension.
