| Abstract: | We construct a polarized Hodge structure on the primitive part of Chen and Ruan's orbifold cohomology  for projective  -orbifolds  satisfying a ``Hard Lefschetz Condition'. Furthermore, the total cohomology  forms a mixed Hodge structure that is polarized by every element of the Kähler cone of  . Using results of Cattani-Kaplan-Schmid this implies the existence of an abstract polarized variation of Hodge structure on the complexified Kähler cone of  . This construction should be considered as the analogue of the abstract polarized variation of Hodge structure that can be attached to the singular cohomology of a crepant resolution of  , in light of the conjectural correspondence between the (quantum) orbifold cohomology and the (quantum) cohomology of a crepant resolution. |
