Can I read K\"ahler-Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII on EtoBox?

K\"ahler-Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII by Hong, Kyusik; Hwang, DongSeon; Park, Kyeong-Dong is a scholarly article available to read on EtoBox.

What is K\"ahler-Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII about?

The wonderful compactification $X_m$ of a symmetric homogeneous space of type AIII$(2,m)$ for each $m \geq 4$ is Fano, and its blowup $Y_m$ along the unique closed orbit is Fano if $m \geq 5$ and Calabi-Yau if $m = 4$. Using a combinatorial criterion for K-polystability of smooth Fano spherical varieties obtained by Delcroix, we prove that $X_m$ admits a K\"ahler-Einstein metric for each $m \geq 4$ and $Y_m$ admits a K\"ahler-Einstein metric if and only if $m = 4, 5$.

Author

Hong, Kyusik; Hwang, DongSeon; Park, Kyeong-Dong

Published

2022

Language

EN