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We prove the existence of Kähler-Einstein metrics on a nonsingular section of the Grassmannian Gr(2, 5) ⊂ ℙ9 by a linear subspace of codimension 3 and on the Fermat hypersurface of degree 6 in 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.

Extremal metrics on del Pezzo threefolds