Twisted jets, motivic measure and orbifold cohomology

Abstract

We introduce the notion of twisted jet on a Deligne-Mumford stack. and study the motivic measure on the space of the twisted $\infty$-jets on a smooth Deligne-Mumford stack. As an application, we prove that two birational minimal models with Gorenstein quotient singularities have the same orbifold cohomology with Hodge structure.