Examples of asymptotically conical Ricci-flat Kahler manifolds

Previously the author has proved that a crepant resolution pi : Y -> X of a Ricci-flat Kahler cone X admits a complete Ricci-flat Kahler metric asymptotic to the cone metric in every Kahler class in H-c(2) (Y, R). These manifolds can be considered to be generalizations of the Ricci-flat ALE Kahler spaces known by the work of P. Kronheimer, D. Joyce and others. This article considers further the problem of constructing examples. We show that every 3-dimensional Gorenstein toric Kahler cone admits a crepant resolution for which the above theorem applies. This gives infinitely many examples of asymptotically conical Ricci-flat manifolds. Then other examples are given of which are crepant resolutions hyper-surface singularities which are known to admit Ricci-flat Kahler cone metrics by the work of C. Boyer, K. Galicki, J. Kollar, and others. We concentrate on 3-dimensional examples. Two families of hypersurface examples are given which are distinguished by the condition b(3)(Y) = 0 or b(3)(Y) not equal 0.