关于阿贝尔簇的子簇的符号欧拉示性数性质
On the signed Euler characteristic property for subvarieties of abelian varieties
摘要：
给出了复阿贝尔簇的纯维闭子簇具有符号交同调欧拉示性数的初等证明。我们还表明，这样的子品种，而且，是当地的完全交叉，有一个签署的欧拉-庞加莱特性。我们的论点依赖于建设的圆值莫尔斯函数在这样的空间，并使用在一个基本的方式分层莫尔斯理论的Goresky-MacPherson。我们的方法也适用于（只有微小的修改）证明类似的声明，在分析的背景下，即，对于紧致复环面的子簇。我们的结果可以用一般的反常层理论来证明。
英文摘要：
We give an elementary proof of the fact that a pure-dimensional closed subvariety of a complex abelian variety has a signed intersection homology Euler characteristic. We also show that such subvarieties which, moreover, are local complete intersections, have a signed Euler-Poincare characteristic. Our arguments rely on the construction of circle-valued Morse functions on such spaces, and use in an essential way the stratified Morse theory of Goresky-MacPherson. Our approach also applies (with only minor modifications) for proving similar statements in the analytic context, i.e., for subvarieties of compact complex tori. Alternative proofs of our results can be given by using the general theory of perverse sheaves.
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