Rigidity of pairs of rational homogeneous spaces of Picard number $1$ and analytic continuation of geometric substructures on uniruled projective manifolds

2019 ◽  
Vol 112 (2) ◽  
pp. 263-345 ◽  
Author(s):  
Ngaiming Mok ◽  
Yunxin Zhang
Keyword(s):  
Analytic Continuation ◽  
Homogeneous Spaces ◽  
Picard Number ◽  
Projective Manifolds

scholarly journals Kähler–Einstein Metrics on Smooth Fano Symmetric Varieties with Picard Number One

Mathematics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 102
Author(s):  
Jae-Hyouk Lee ◽  
Kyeong-Dong Park ◽  
Sungmin Yoo
Keyword(s):  
Einstein Metrics ◽  
Homogeneous Spaces ◽  
Picard Number ◽  
Spherical Varieties ◽  
Symmetric Varieties ◽  
Moment Polytope ◽  
Kähler Einstein Metrics ◽  
Moment Polytopes

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.

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