映射芽扰动的上同调连通性
Cohomological connectivity of perturbations of map-germs
摘要：
设$f\colon (\mathbb C^n,S)\to (\mathbb C^p,0)$是一个有限映象芽，其中$n<p$和$Y_δ$是小扰动$f_δ$的象.我们发现，减少上同调的$Y_δ$集中在一定范围内的程度所确定的尺寸的不稳定轨迹的$f$。在$n\geq p$的情况下，我们得到一个类似的结果，用$\mathcal K$ -有限性代替有限性，用判别式$Δ(f_δ)$代替$Y_δ$。我们还研究了与扰动$f_δ$相关的单值性。
英文摘要：
Let $f\colon (\mathbb C^n,S)\to (\mathbb C^p,0)$ be a finite map-germ with $n<p$ and $Y_δ$ the image of a small perturbation $f_δ$. We show that the reduced cohomology of $Y_δ$ is concentrated in a range of degrees determined by the dimension of the instability locus of $f$. In the case $n\geq p$ we obtain an analogous result, replacing finiteness by $\mathcal K$-finiteness and $Y_δ$ by the discriminant $Δ(f_δ)$. We also study the monodromy associated to the perturbation $f_δ$.
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