余丛空间中Schubert簇的Mather类和余正规空间
Mather classes and conormal spaces of Schubert varieties in cominuscule spaces
摘要：
设$G/P$是复复可微旗流形.证明了在$G/P$中Schubert簇的环面等变Mather类的一个型无关公式，以及通过自然投影$G/Q \to G/P$拉回的Schubert簇的一个型无关公式.我们应用这一发现公式的局部欧拉障碍的舒伯特品种，并为环面等变本地化的余正规空间的这些舒伯特品种。我们猜想积极的性质，当地的欧拉障碍和舒伯特展开的马瑟类。利用Boe和Fu关于Schubert簇的交同调层的特征圈的结果，我们在许多情况下检验了这些结果。我们还猜想某些“Mather多项式”在一般的Lie型中是单峰的，而在A型中是对数凹的。
英文摘要：
Let $G/P$ be a complex cominuscule flag manifold. We prove a type independent formula for the torus equivariant Mather class of a Schubert variety in $G/P$, and for a Schubert variety pulled back via the natural projection $G/Q \to G/P$. We apply this to find formulae for the local Euler obstructions of Schubert varieties, and for the torus equivariant localizations of the conormal spaces of these Schubert varieties. We conjecture positivity properties for the local Euler obstructions and for the Schubert expansion of Mather classes. We check the conjectures in many cases, by utilizing results of Boe and Fu about the characteristic cycles of the intersection homology sheaves of Schubert varieties. We also conjecture that certain `Mather polynomials' are unimodal in general Lie type, and log concave in type A.
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