A decomposition theorem for $\mathbb{Q}$-Fano Kähler–Einstein varieties
Let $X$ be a $\mathbb{Q}$-Fano variety admitting a Kähler–Einstein metric. We prove that up to a finite quasi-étale cover, $X$ splits isometrically as a product of Kähler–Einstein $\mathbb{Q}$-Fano varieties whose tangent sheaf is stable with respect to the anticanonical polarization. This relies am...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2024-06-01
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| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.612/ |
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| Summary: | Let $X$ be a $\mathbb{Q}$-Fano variety admitting a Kähler–Einstein metric. We prove that up to a finite quasi-étale cover, $X$ splits isometrically as a product of Kähler–Einstein $\mathbb{Q}$-Fano varieties whose tangent sheaf is stable with respect to the anticanonical polarization. This relies among other things on a very general splitting theorem for algebraically integrable foliations. We also prove that the canonical extension of $T_X$ by $\mathscr{O}_X$ is polystable with respect to the anticanonical polarization. |
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| ISSN: | 1778-3569 |