论文标题
Kähler-Einstein指标与Picard第一
Kähler-Einstein metrics on smooth Fano symmetric varieties with Picard number one
论文作者
论文摘要
对称品种是对称均匀空间的正常均等开放式嵌入，它们是球形品种的有趣示例。我们证明，所有光滑的Fano对称品种都使用PICARD第一，通过使用Delcroix获得的Fano球形品种的K稳定性来允许Kähler-Einstein指标。为此，我们介绍它们的代数矩多型，并相对于Duistermaat-Heckman度量计算每个矩多层的Barycenter。
Symmetric varieties are normal equivarient open embeddings of symmetric homogeneous spaces, and they are interesting examples of spherical varieties. We prove that all smooth Fano symmetric varieties with Picard number one admit Kähler-Einstein metrics by using a combinatorial criterion for K-stability of Fano spherical varieties obtained by Delcroix. For this purpose, we present their algebraic moment polytopes and compute the barycenter of each moment polytope with respect to the Duistermaat-Heckman measure.
