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

2020/11/30 by Jae-Hyouk Lee, Kyeong-Dong Park, Sungmin Yoo
Mathematics · #Algebraic Geometry and Number Theory #Algebraic number #Algebraic variety #Fano plane #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homogeneous #Moment (physics) #Polytope #math.AG #math.DG #msc:14M27 #msc:32Q20 #msc:53C25

paper · pdf · doi:10.3390/math9010102

published as Mathematics (2021), Vol. 9, no. 1, 102 · 13 pages, 6 figures

openalex created_date 2020/12/07 · openalex publication_date 2021/01/05 · arxiv created 2021/01/07 · arxiv updated 2021/01/08 · openalex updated_date 2026/08/05

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.

Citations

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