Extremal metrics on del Pezzo threefolds

Abstract

We prove the existence of Kahler-Einstein metrics on a nonsingular section of the Grassmannian $\mathrm{Gr}(2,5)\subset {\mathbb{P}}^9$ by a linear subspace of codimension 3, and the Fermat hypersurface of degree 6 in $\mathbb{P}(1,1,1,2,3)$. We also show that a global log canonical threshold of the Mukai--Umemura variety is equal to 1/2.

16 pages, dedication is changed, because Vasily Iskovskikh passed away on 4th January 2009