论文标题
库伯特品种在cominuscule空间中的MATHER类和综合空间
Mather classes and conormal spaces of Schubert varieties in cominuscule spaces
论文作者
论文摘要
令$ g/p $为复杂的cominuscule标志歧管。我们证明了一种类型的独立公式，用于$ g/p $ schubert variect的圆环的马瑟级，以及通过自然投影$ g/q \ to to g/p $撤回的舒伯特品种。我们将其应用于舒伯特品种的局部欧拉障碍物的公式，以及这些舒伯特品种的共态空间的圆环等效性。我们猜想了局部欧拉障碍物和舒伯特扩大马瑟阶级的阳性性能。在许多情况下，我们通过利用BOE和FU的结果来检查这些猜想，以了解舒伯特品种的交叉点同源性皮带的特征周期。我们还猜想某些“ Mather多项式”在一般谎言类型中是单峰。
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.
