Kähler–Einstein Fano threefolds of degree 22

Abstract

We study the problem of existence of Kähler–Einstein metrics on smooth Fano threefolds of Picard rank one and anticanonical degree 22 22 that admit a faithful action of the multiplicative group C ∗ \mathbb {C}^\ast . We prove that, with the possible exception of two explicitly described cases, all such smooth Fano threefolds are Kähler–Einstein.