论文标题
Gysin相干特性类别的独特定理奇异空间
The Uniqueness Theorem for Gysin Coherent Characteristic Classes of Singular Spaces
论文作者
论文摘要
我们建立了一种通用计算方案，专门针对具有横向设置中满足Gysin Axiom的奇异复合代数品种的特征类别类别的系统计算。该方案是明确的几何形状和递归性质，该递归性质终止了我们构造的明确特征亚变量的属。它使我们能够应用舒伯特品种的交点理论，以获得环境格拉曼尼亚同源性的这种特征类别的独特性结果。我们的框架特别适用于Goresky-Macpherson L-Class，借助第一作者在先前的工作中获得的Gysin限制公式。我们说明了我们在通常非主张扩展的奇异舒伯特品种的示例中对L级进行系统计算的方法，而这些schubert品种不满足理性的庞加莱二元性。
We establish a general computational scheme designed for a systematic computation of characteristic classes of singular complex algebraic varieties that satisfy a Gysin axiom in a transverse setup. This scheme is explicitly geometric and of a recursive nature terminating on genera of explicit characteristic subvarieties that we construct. It enables us e.g. to apply intersection theory of Schubert varieties to obtain a uniqueness result for such characteristic classes in the homology of an ambient Grassmannian. Our framework applies in particular to the Goresky-MacPherson L-class by virtue of the Gysin restriction formula obtained by the first author in previous work. We illustrate our approach for a systematic computation of the L-class in terms of normally nonsingular expansions in examples of singular Schubert varieties that do not satisfy Poincaré duality over the rationals.
