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

Jae Hyouk Lee, Kyeong Dong Park, Sungmin Yoo

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Article number102
Pages (from-to)1-15
Number of pages15
JournalMathematics
Volume9
Issue number1
DOIs
StatePublished - 1 Jan 2021

Keywords

  • Kähler–Einstein metrics
  • Moment polytopes
  • Symmetric varieties

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