论文标题
扭曲的Kähler-Einstein指标在国旗品种上
Twisted Kähler-Einstein metrics on flag varieties
论文作者
论文摘要
在本文中，我们描述了在国旗品种上不变的扭曲Kähler-Einstein（TKE）指标。我们还探讨了我们主要结果证明的一些想法的某些应用，以证明存在不变的恒定标态曲率kähler指标。另外，我们为最大的RICCI下限提供了一个任意Kähler班级的最大RICCI下限的精确描述。通过此描述，我们建立了一些与Kähler指标的最佳卷上限相关的不平等现象，仅使用Lie理论中的工具。此外，我们描述了几个示例的TKE指标集，包括完整的标志品种，$ \ mathbb {p}^{n+1} $的切线捆绑包的项目化以及具有Picard数字$ 2 $的国旗品种的家属。
In this paper, we describe invariant twisted Kähler-Einstein (tKE) metrics on flag varieties. We also explore some applications of the ideas involved in the proof of our main result to the existence of invariant twisted constant scalar curvature Kähler metrics. Also, we provide a precise description for the greatest Ricci lower bound of an arbitrary Kähler class on a flag variety. By means of this description, we establish some inequalities related to optimal volume upper bounds for Kähler metrics just using tools from Lie theory. Further, we describe the set of tKE metrics for several examples, including full flag varieties, the projectivization of the tangent bundle of $\mathbb{P}^{n+1}$, and families of flag varieties with Picard number $2$.
