A Matsushima theorem for K-polystable polarised smooth Fano threefolds
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866914498791604224 |
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| author | Abban, Hamid Cascini, Paolo Cheltsov, Ivan |
| author_facet | Abban, Hamid Cascini, Paolo Cheltsov, Ivan |
| contents | We prove that if $X$ is a smooth Fano threefold and $L$ is an ample $\mathbb{Q}$-divisor such that $(X,L)$ is K-polystable, then the automorphism group $\operatorname{Aut}(X)$ is reductive. This verifies the reductivity statement predicted by the Yau--Tian--Donaldson conjecture in the setting of smooth Fano threefolds with arbitrary ample polarisation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20440 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Matsushima theorem for K-polystable polarised smooth Fano threefolds Abban, Hamid Cascini, Paolo Cheltsov, Ivan Algebraic Geometry We prove that if $X$ is a smooth Fano threefold and $L$ is an ample $\mathbb{Q}$-divisor such that $(X,L)$ is K-polystable, then the automorphism group $\operatorname{Aut}(X)$ is reductive. This verifies the reductivity statement predicted by the Yau--Tian--Donaldson conjecture in the setting of smooth Fano threefolds with arbitrary ample polarisation. |
| title | A Matsushima theorem for K-polystable polarised smooth Fano threefolds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2604.20440 |