论文标题
在舒伯特品种的圆环商上
On the torus quotients of Schubert varieties
论文作者
论文摘要
在本文中，我们考虑了舒伯特品种的git商，以实现最大圆环的作用。我们描述了舒伯特（Schubert）的微小品种，该品种在光滑的基因座中包含了可半固定的基因座。结果，我们研究了格拉斯曼尼亚人的舒伯特品种的圆环商的光滑度。我们还证明，对于均匀空间中的任何舒伯特的曲折商$ sl（n，\ mathbb c）/p $，相对于线条捆绑$ \ mathcal $ \ mathcal l_ {α_0} $，投影态度是正常的，并且商的空间是投射空间\ mathbb c）$与最高的根$α_0$相关。
In this paper, we consider the GIT quotients of Schubert varieties for the action of a maximal torus. We describe the minuscule Schubert varieties for which the semistable locus is contained in the smooth locus. As a consequence, we study the smoothness of torus quotients of Schubert varieties in the Grassmannian. We also prove that the torus quotient of any Schubert variety in the homogeneous space $SL(n, \mathbb C)/P$ is projectively normal with respect to the line bundle $\mathcal L_{α_0}$ and the quotient space is a projective space, where the line bundle $\mathcal L_{α_0}$ and the parabolic subgroup $P$ of $SL (n, \mathbb C)$ are associated to the highest root $α_0$.
