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

Stéphane Druel; Henri Guenancia; Mihai Păun

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arXiv · 2008.05352

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

Stéphane Druel·Henri Guenancia·Mihai Păun

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Abstract

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 semistable with respect to the anticanonical polarization.

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Stéphane Druel, Henri Guenancia, Mihai Păun. 2020-08-12. A decomposition theorem for $\mathbb Q$-Fano Kähler-Einstein varieties. https://arxiv.org/abs/2008.05352

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