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

Stéphane Druel, Henri Guenancia, Mihai Păun

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 $…