Automorphism groups of toroidal horospherical varieties
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917320687878144 |
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| author | Barban, Lorenzo Hwang, DongSeon Kwon, Minseong |
| author_facet | Barban, Lorenzo Hwang, DongSeon Kwon, Minseong |
| contents | We establish a structure theorem for the connected automorphism groups of smooth complete toroidal horospherical varieties, that is, toric fibrations over rational homogeneous spaces. The key ingredient is a characterization of the Demazure roots of toric fibers that extend to the total space. In particular, we provide a criterion for the reductivity of the connected automorphism groups of such varieties. As an application, we prove the K-unstability of certain $\mathbb{P}^1$-bundles over rational homogeneous spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07879 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Automorphism groups of toroidal horospherical varieties Barban, Lorenzo Hwang, DongSeon Kwon, Minseong Algebraic Geometry 14M27, 14M25, 14J50, 14L30 We establish a structure theorem for the connected automorphism groups of smooth complete toroidal horospherical varieties, that is, toric fibrations over rational homogeneous spaces. The key ingredient is a characterization of the Demazure roots of toric fibers that extend to the total space. In particular, we provide a criterion for the reductivity of the connected automorphism groups of such varieties. As an application, we prove the K-unstability of certain $\mathbb{P}^1$-bundles over rational homogeneous spaces. |
| title | Automorphism groups of toroidal horospherical varieties |
| topic | Algebraic Geometry 14M27, 14M25, 14J50, 14L30 |
| url | https://arxiv.org/abs/2602.07879 |