Global Torelli theorem for irreducible symplectic orbifolds

TL;DR

This paper extends the global Torelli theorem to irreducible symplectic orbifolds, generalizing key concepts like twistor space and projectivity criteria within the Kähler setting.

Contribution

It generalizes Verbitsky's Torelli theorem to symplectic orbifolds and adapts existing proofs and criteria for this broader class of geometric objects.

Findings

Generalization of the Torelli theorem to symplectic orbifolds

Extension of twistor space concepts to orbifolds

New projectivity criterion for irreducible symplectic orbifolds

Abstract

We propose a generalization of Verbitsky's global Torelli theorem in the framework of compact K\"ahler irreducible holomorphically symplectic orbifolds by adapting Huybrechts' proof (arXiv:1106.5573). As intermediate step needed, we also provide a generalization of the twistor space and the projectivity criterion based on works of Campana (arXiv:math/0402243) and Huybrechts (arXiv:math/0106014) respectively.