Kähler–Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII-Reference-Cited by-同舟云学术

Kähler–Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII

Published:2024-04-10 Issue:07 Volume:35 Page:
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

Hong Kyusik¹^ORCID,Hwang DongSeon²^ORCID,Park Kyeong-Dong³^ORCID

Affiliation:

1. Department of Mathematics Education, Jeonju University, Jeonju 55069, Republic of Korea

2. Center for Complex Geometry, Institute for Basic Science, Daejeon 34126, Republic of Korea

3. Department of Mathematics and Research Institute of Natural Science/Research Institute of Molecular Alchemy, Gyeongsang National University, Jinju 52828, Republic of Korea

Abstract

The wonderful compactification [Formula: see text] of a symmetric homogeneous space of type AIII[Formula: see text] for each [Formula: see text] is Fano, and its blowup [Formula: see text] along the unique closed orbit is Fano if [Formula: see text] and Calabi–Yau if [Formula: see text]. Using a combinatorial criterion for K-polystability of smooth Fano spherical varieties obtained by Delcroix, we prove that [Formula: see text] admits a Kähler–Einstein metric for each [Formula: see text] and [Formula: see text] admits a Kähler–Einstein metric if and only if [Formula: see text].

Funder

National Research Foundation of Korea

Samsung Science and Technology Foundation

Gyeongsang National University

Ministry of Education

Publisher

World Scientific Pub Co Pte Ltd

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X2450023X

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