Resolutions of cones over Einstein-Sasaki spaces

Abstract Recently an explicit resolution of the Calabi–Yau cone over the inhomogeneous five-dimensional Einstein–Sasaki space Y 2 , 1 was obtained. It was constructed by specialising the parameters in the BPS limit of recently-discovered Kerr–NUT–AdS metrics in higher dimensions. We study the occurrence of such non-singular resolutions of Calabi–Yau cones in a more general context. Although no further six-dimensional examples arise as resolutions of cones over the L p q r Einstein–Sasaki spaces, we find general classes of non-singular cohomogeneity-2 resolutions of higher-dimensional Einstein–Sasaki spaces. The topologies of the resolved spaces are of the form of an R 2 bundle over a base manifold that is itself an S 2 bundle over an Einstein–Kahler manifold.