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.
Original language | English |
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Article number | 102 |
Pages (from-to) | 1-15 |
Number of pages | 15 |
Journal | Mathematics |
Volume | 9 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jan 2021 |
Bibliographical note
Funding Information:Funding: Jae-Hyouk Lee was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2019R1F1A1058962). Kyeong-Dong Park was supported by the Institute for Basic Science (IBS-R003-D1) and by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2019R1A2C3010487). Sungmin Yoo was supported by the Institute for Basic Science (IBS-R003-D1).
Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.
Keywords
- Kähler–Einstein metrics
- Moment polytopes
- Symmetric varieties