Ricci-flat K'ahler metrics on crepant resolutions of K'ahler cones

摘要

We prove that a crepant resolution of a Ricci-flat K\"ahler cone X admits acomplete Ricci-flat K\"ahler metric asymptotic to the cone metric in everyK\"ahler class in H^2_c(Y,R). This result contains as a subcase the existenceof ALE Ricci-flat K\"ahler metrics on crepant resolutions of X=C^n /G, where Gis a finite subgroup of SL(n,C). We consider the case in which X is toric. A result of A. Futaki, H. Ono, andG. Wang guarantees the existence of a Ricci-flat K\"ahler cone metric if X isGorenstein. We use toric geometry to construct crepant resolutions.