论文标题
订单两种元素的中央器的国旗品种中的轨道封闭：a，b，d型的正态性和分辨率
Orbit closures in flag varieties for the centralizer of an order-two nilpotent element : normality and resolutions for types A, B, D
论文作者
论文摘要
令G为经典A，B，D和E中的还原代数群，为其lie代数的元素，其Z中的Centeriser在G中进行伴随作用。我们假设e用二级阶的nilpotent矩阵识别，该矩阵保证了g的标志品种中的z孔数量是有限的。对于B型，d在特征二中，我们还假设E的图像完全各向同性。我们表明，这种轨道的任何封闭都是正常的。我们还证明Y是Cohen-Macaulay，只要基本场具有特征性的零，并且Cohen-Macaulays仍然是A型的任何特征。我们的工作概括了N. Perrin和E. Smirnov在弹簧纤维上的结果（[PS12]）。
Let G be a reductive algebraic group in classical types A, B, D and e be an element of its Lie algebra with Z its centraliser in G for the adjoint action. We suppose that e identifies with an nilpotent matrix of order two, which guarantees the number of Z-orbits in the flag variety of G is finite. For types B, D in characteristic two, we also suppose the image of e is totally isotropic. We show that any closure Y of such orbit is normal. We also prove that Y is Cohen-Macaulay with rational singularities provided that the base field is of characteristic zero, and that Cohen-Macaulayness remains in any characteristic for type A. We exhibit a birational, rational morphism onto Y involving Schubert varieties. Our work generalizes a result by N. Perrin and E. Smirnov on Springer fibers ([PS12]).
