Automorphisms of Crepant Resolutions for Quotient Spaces

摘要

Let X be a Kahler manifold and G be a finite group of biholomorphic volumepreserving automorphisms of X. Let pi : (X/G)(tilde) -> X/G be a crepant resolution of the orbit space X/G (i.e. the pullback of the dualizing sheaf of X/G is the canonical bundle of (X/G)(tilde)). In this paper the authors shall propose a formula designed for the study of manifolds for which the pair (X,G) admits a symmetry h. This formula allows one to calculate the Lefshetz number of an automorphism acting on a crepant resolution of the quotient.