Kähler-Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909221263507456 |
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| author | Hong, Kyusik Hwang, DongSeon Park, Kyeong-Dong |
| author_facet | Hong, Kyusik Hwang, DongSeon Park, Kyeong-Dong |
| contents | 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 $m = 4, 5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_14720 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Kähler-Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII Hong, Kyusik Hwang, DongSeon Park, Kyeong-Dong Algebraic Geometry Differential Geometry Primary: 14M27, 32Q20, Secondary: 32M12, 32Q26, 53C55 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 $m = 4, 5$. |
| title | Kähler-Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII |
| topic | Algebraic Geometry Differential Geometry Primary: 14M27, 32Q20, Secondary: 32M12, 32Q26, 53C55 |
| url | https://arxiv.org/abs/2209.14720 |