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Kähler-Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII
- Hong, Kyusik;
- Hwang, DongSeon;
- Park, Kyeong-Dong
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0초록
The wonderful compactification Xm of a symmetric homogeneous space of type AIII(2,m) for each m >= 4 is Fano, and its blowup Ym along the unique closed orbit is Fano if m >= 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 Xm admits a Kahler-Einstein metric for each m >= 4 and Ym admits a Kahler-Einstein metric if and only if m = 4, 5.
키워드
Symmetric variety; wonderful compactification; Kahler-Einstein metric; K-stability; moment polytope; spherical variety; greatest Ricci lower bound; KAHLER-EINSTEIN METRICS; MONGE-AMPERE EQUATIONS; GREATEST LOWER BOUNDS; RICCI CURVATURE; K-STABILITY; COMPLEX-SURFACES
- 제목
- Kähler-Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII
- 저자
- Hong, Kyusik; Hwang, DongSeon; Park, Kyeong-Dong
- 발행일
- 2024-06
- 유형
- Article
- 권
- 35
- 호
- 07