A decomposition theorem for $\mathbb Q$-Fano Kähler-Einstein varieties - Archive ouverte HAL
Article Dans Une Revue Comptes Rendus. Mathématique Année : 2024

A decomposition theorem for $\mathbb Q$-Fano Kähler-Einstein varieties

Résumé

Let $X$ be a $\mathbb Q$-Fano variety admitting a K\"ahler-Einstein metric. We prove that up to a finite quasi-\'etale cover, $X$ splits isometrically as a product of K\"ahler-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 semistable with respect to the anticanonical polarization.
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Dates et versions

hal-02922651 , version 1 (26-08-2020)

Identifiants

Citer

Stéphane Druel, Henri Guenancia, Mihai Păun. A decomposition theorem for $\mathbb Q$-Fano Kähler-Einstein varieties. Comptes Rendus. Mathématique, 2024, 362 (S1), pp.93-118. ⟨10.5802/crmath.612⟩. ⟨hal-02922651⟩
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