Inclusion-exclusion and Segre classes, II

Inclusion-exclusion and Segre classes

We propose a variation of the notion of Segre class, by forcing a naive `inclusion-exclusion' principle to hold. The resulting class is computationally tractable, and is closely related to Chern-Schwartz-MacPherson classes. We deduce several general properties of the new class from this relation, and obtain an expression for the Milnor class of a scheme in terms of this class.

Cohomological and motivic inclusion-exclusion

We categorify the inclusion-exclusion principle for partially ordered topological spaces and schemes to a filtration on the derived category of sheaves. As a consequence, we obtain functorial spectral sequences that generalize the two spectral sequences of a stratified space and certain Vassiliev-type spectral sequences; we also obtain Euler characteristic analogs in the Grothendieck ring of varieties. As an application, we give an algebro-geometric proof of Vakil and Wood's homological stability conjecture for the space of smooth hypersurface sections of a smooth projective variety. In charac…

点希尔伯特概型上 tautological 层的容斥原理

An inclusion-exclusion principle for tautological sheaves on Hilbert schemes of points

本研究证明双点退化纤维上点希尔伯特概型tautological层的欧拉特征满足容斥型等式，推导出光滑真代数空间上对应欧拉特征的通用多项式存在性，并将Zhou的相关猜想约简至射影空间乘积情形，主要工具为优态退化与代数配边。

Schubert 拼图与可积性 II：乘性动机 Segre 类

Schubert puzzles and integrability II: multiplying motivic Segre classes

本文在有限 q 下给出 Schubert 拼图规则中矩阵元的上同调解释，证明其计算动机 Segre 类乘积，并通过 Nakajima 箭图簇的拉格朗日卷积阐明拼图计算，避免了 d=3,4 的发散问题。