Addendum to: A simultaneous Frobenius splitting for closures of conjugacy classes of nilpotent matrices, by V. B. Mehta and Wilberd van der Kallen

A Bruhat atlas for the Mehta-van der Kallen stratification of $T^* GL_n/B$

Mehta and van der Kallen put a Frobenius splitting on the type A cotangent bundle $T^* GL_n/B$, thereby defining a stratification by compatibly split subvarieties, and they determined a few of the elements of this stratification. We embed $T^* GL_n/B$ as a stratum in a larger stratified (and Frobenius split) space $GL_n/B \times Mat_n$ whose stratification we determine, thereby giving a full description of the one of Mehta-van der Kallen. The main technique is to endow $GL_n/B \times Mat_n$ with a Bruhat atlas, covering it with open sets that are stratified-isomorphic to Bruhat cells (in $GL_{…

GL_n 旗簇余切丛的 Frobenius 分裂与上同调消失

A Frobenius splitting and cohomology vanishing for the cotangent bundles of the flag varieties of GL_n

本文证明了 GL_n 旗丛余切丛的 Frobenius 分裂具有最高次数，给出了分量函数公式并证明其在例外轨迹上消失，进而得出与支配权相关线丛的高阶上同调群为零。