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

Jae-Hyouk Lee, Kyeong-Dong Park and Sungmin Yoo
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Jae-Hyouk Lee: Department of Mathematics, Ewha Womans University, Seodaemun-gu, Seoul 03760, Korea
Kyeong-Dong Park: School of Mathematics, Korea Institute for Advanced Study (KIAS), Dongdaemun-gu, Seoul 02455, Korea
Sungmin Yoo: Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang 37673, Korea

Mathematics, 2021, vol. 9, issue 1, 1-15

Abstract: 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.

Keywords: Kähler–Einstein metrics; symmetric varieties; moment polytopes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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