Global Torelli theorem for irreducible symplectic orbifolds

Abstract We propose a generalization of Verbitsky's global Torelli theorem in the framework of compact Kahler irreducible holomorphically symplectic orbifolds by adapting Huybrechts' proof [17] . As intermediate step needed, we also provide a generalization of the twistor space and the projectivity criterion based on works of Campana [7] and Huybrechts [22] respectively.