Kähler–einstein metrics on smooth fano symmetric varieties with picard number one

Jae Hyouk Lee; Kyeong Dong Park; Sungmin Yoo

doi:10.3390/math9010102

Kähler–einstein metrics on smooth fano symmetric varieties with picard number one

Jae Hyouk Lee, Kyeong Dong Park, Sungmin Yoo

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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
Article number	102
Pages (from-to)	1-15
Number of pages	15
Journal	Mathematics
Volume	9
Issue number	1
DOIs	https://doi.org/10.3390/math9010102
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

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10.3390/math9010102

Cite this

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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 K{\"a}hler–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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author = "Lee, {Jae Hyouk} and Park, {Kyeong Dong} and Sungmin Yoo",

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N2 - 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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KW - Symmetric varieties

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Kähler–einstein metrics on smooth fano symmetric varieties with picard number one

Abstract

Bibliographical note

Keywords

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