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Working paper

Kaehler-Einstein Fano threefolds of degree 22

We study the problem of existence of K\"ahler--Einstein metrics on smooth Fano threefolds of Picard rank one and anticanonical degree 22 that admit a faithful action of the multiplicative group ℂ∗. We prove that, except possibly two explicitly described cases, all such smooth Fano threefolds are K\"ahler--Einstein.