论文标题
Kähler-Einstein type aiii型的光滑Fano环形对称品种的指标
Kähler-Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII
论文作者
论文摘要
奇妙的紧凑型$ x_m $的对称同质型aiii $（2，m）$的对称均值空间（2，m）$是fano，而它的blowup $ y_m $沿着独特的封闭轨道为fano，如果$ m \ geq 5 $ 5 $ and calabi-yau，则如果$ m = $ m = 4 $ = 4 $。使用Delcroix获得的光滑Fano球形品种的K-Politerion的组合标准，我们证明$ x_m $允许每个$ m \ geq 4 $ and $ y_m $ akähler-einstein衡量标准，如果$ m \ y_m $承认akähler-einstein Metric，则仅如果$ = $ m = m = 4 $ = 4，5 $ 5 $ 5 $ 5 $。
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 Kähler-Einstein metric for each $m \geq 4$ and $Y_m$ admits a Kähler-Einstein metric if and only if $m = 4, 5$.
