On the K\"ahler cone of irreducible symplectic orbifolds

TL;DR

This paper extends the global Torelli theorem and K"ahler cone results to irreducible symplectic orbifolds, proposing a new perspective on mirror symmetry as an involution on moduli spaces.

Contribution

It generalizes key theorems and concepts from smooth to orbifold cases, introducing a novel approach to mirror symmetry in this context.

Findings

Generalization of the Hodge version of the global Torelli theorem to orbifolds

Extension of K"ahler cone and wall divisor concepts to orbifolds

New definition of mirror symmetry as an involution on moduli space

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.