On the K\"ahler cone of irreducible symplectic orbifolds

Abstract

We generalize the Hodge version of the global Torelli theorem in the framework of irreducible symplectic orbifolds. We also propose a generalization of several results related to the K\"ahler cone and the notion of wall divisors introduced in the smooth case by Mongardi. As an application we propose a definition of the mirror symmetry as an involution on a moduli space; this construction is also new in the smooth case.