论文标题
舒伯特品种的切线空间和Tinvariant曲线
Tangent spaces and T-invariant curves of Schubert varieties
论文作者
论文摘要
通过T固定点，Schubert品种中的Tinvariant曲线集相对容易就其重量来表征，但是切线空间更加困难。我们证明，切线空间的重量包含在T-非定量曲线的重量产生的有理锥中。在简单的类型中，如果“理性”被“积分”取代，则这是正确的。我们还获得了各个重量分别空间的条件，即T-invariant曲线的重量以及平滑度标准。结果依赖于模棱两可的K理论，以及对根的可分解性概念的研究。
The set of T-invariant curves in a Schubert variety through a T-fixed point is relatively easy to characterize in terms of its weights, but the tangent space is more difficult. We prove that the weights of the tangent space are contained in the rational cone generated by the weights of the T-invariant curves. In simply laced types, this remains true if "rational" is replaced by "integral". We also obtain conditions under which every weight of the tangent space is the weight of a T-invariant curve, as well as a smoothness criterion. The results rely on equivariant K-theory, as well as the study of different notions of decomposability of roots.
