Resolutions of non-regular Ricci-flat Kähler cones

We present explicit constructions of complete Ricci-flat Kähler metrics that are asymptotic to cones over non-regular Sasaki-Einstein manifolds. The metrics are constructed from a complete Kähler-Einstein manifold (V, gV ) of positive Ricci curvature and admit a Hamiltonian two-form of order two. We obtain Ricci-flat Kähler metrics on the total spaces of (i) holomorphic C/Zp orbifold fibrations over V , (ii) holomorphic orbifold fibrations over weighted projective spaces WCP, with generic fibres being the canonical complex cone over V , and (iii) the canonical orbifold line bundle over a family of Fano orbifolds. As special cases, we also obtain smooth complete Ricci-flat Kähler metrics on the total spaces of (a) rank two holomorphic vector bundles over V , and (b) the canonical line bundle over a family of geometrically ruled Fano manifolds with base V . When V = CP our results give Ricci-flat Kähler orbifold metrics on various toric partial resolutions of the cone over the Sasaki-Einstein manifolds Y p,q. ∗ On leave from: Blackett Laboratory, Imperial College, London SW7 2AZ, U.K.