Resolutions of non-regular Ricci-flat Kahler cones

We present explicit constructions of complete Ricci-flat Kahler metrics that are asymptotic to cones over non-regular Sasaki-Einstein manifolds. The metrics are constructed from a complete Kahler-Einstein manifold (V, g(v)) of positive Ricci curvature and admit a Hamiltonian two-form of order two. We obtain Ricci-flat Kahler metrics on the total spaces of (i) holomorphic C-2/Z(p) orbifold fibrations over V, (ii) holomorphic orbifold fibrations over weighted projective spaces WCPI, 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 Kahler 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 = CP1 our results give Ricci-flat Kahler orbifold metrics on various toric partial resolutions of the cone over the Sasaki-Einstein manifolds y(p,q). (C) 2009 Elsevier B.V. All rights reserved.