Euler Obstruction and Defects of Functions on Singular Varieties
Euler Obstruction and Defects of Functions on Singular Varieties
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奇异簇上的欧拉阻碍和函数缺陷
DOI：
10.1112/s0024610704005447
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
J. Seade
中科院分区：
文献类型：
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作者：
J. Brasselet;D. Massey;A. J. Parameswaran;J. Seade
几位作者已经证明了局部欧拉障碍的Lefschetz型公式。特别是，这种类型的结果已被证明是相当于说，当地欧拉障碍，作为一个可构造的功能，满足当地欧拉条件（在双变理论）关于一般线性形式。本文的目的是确定是什么阻止了当地欧拉障碍满足当地欧拉条件的功能是奇异的考虑点。这是通过这些函数的不变量（或“缺陷”）来衡量的。这个缺陷的解释是在消失的周期，这使得它可以计算代数。当函数具有孤立奇点时，不变量可以通过障碍理论几何地定义。这个不变量统一了函数的Milnor数和解析集的局部欧拉阻塞的通常概念。
Several authors have proved Lefschetz type formulas for the local Euler obstruction. In particular, a result of this type has been proved that turns out to be equivalent to saying that the local Euler obstruction, as a constructible function, satisfies the local Euler condition (in bivariant theory) with respect to general linear forms. The purpose of the paper is to determine what prevents the local Euler obstruction from satisfying the local Euler condition with respect to functions which are singular at the considered point. This is measured by an invariant (or ‘defect’) of such functions. An interpretation of this defect is given in terms of vanishing cycles, which allows it to be calculated algebraically. When the function has an isolated singularity, the invariant can be defined geometrically, via obstruction theory. This invariant unifies the usual concepts of the Milnor number of a function and the local Euler obstruction of an analytic set.