标题： 相对布鲁斯-罗伯茨数和陈障碍 显示英文标题

标题： Relative Bruce-Roberts number and Chern obstruction

摘要： 设$(X,0)$是$(\mathbb C^n,0)$中一个等维数解析集的芽，$f=(f_1,f_2)$是在$X.$上定义到平面的映射芽。在本工作中，我们研究与对$(f,X),$相关的拓扑不变量，其中包括$f,$ $Eu_{f,X}(0),$ 的欧拉阻碍，在适当的假设下，还包括与$f.$相关的微分形式族的陈数。这些不变量提供的拓扑信息是有用的，尽管难以计算。 本文的目的是引入Bruce-Roberts数和相对Bruce-Roberts数作为有用的代数工具，以捕捉由欧拉障碍和陈数给出的拓扑信息。当$X,\, X\cap f_2^{-1}(0),\, X\cap f_2^{-1}(0)\cap f_1^{-1}(0)$为ICIS时，给出了闭合公式。在最后一部分，对于二维ICIS$(X,0) \subset (\mathbb C^n,0),$，我们应用我们的结果来给出一个稳定化的一个$\mathcal A$-有限映射芽$f=(f_1, f_2): (X,0) \to (\mathbb C^2,0).$的尖点数$c(f|_X)$的替代描述。$c(f|_X)$的公式首次在[21]中给出。 显示英文摘要

摘要： Let $(X,0)$ be the germ of an equidimensional analytic set in $(\mathbb C^n,0)$ and $f=(f_1,f_2)$ a map-germ into the plane defined on $X.$ In this work, we investigate topological invariants associated to the pair $(f,X),$ among them, the Euler obstruction of $f,$ $Eu_{f,X}(0),$ and under convenient assumptions, the Chern number of families of differential forms associated to $f.$ The topological information provided by these invariants is useful, although difficult to calculate. The aim of the paper is to introduce the Bruce-Roberts and the relative Bruce-Roberts numbers as useful algebraic tools to capture the topological information giving by the Euler obstruction and the Chern numbers. Closed formulas are given when $X,\, X\cap f_2^{-1}(0),\, X\cap f_2^{-1}(0)\cap f_1^{-1}(0)$ are ICIS. In the last section, for a 2-dimensional ICIS $(X,0) \subset (\mathbb C^n,0),$ we apply our results to give an alternative description for the number of cusps $c(f|_X)$ of an stabilization of an $\mathcal A$-finite map-germ $f=(f_1, f_2): (X,0) \to (\mathbb C^2,0).$ A formula for $c(f|_X)$ was first given in [21].