A global Torelli theorem for singular symplectic varieties

@article{Bakker2016AGT,
  title={A global Torelli theorem for singular symplectic varieties},
  author={Benjamin Bakker and Christian Lehn},
  journal={arXiv: Algebraic Geometry},
  year={2016}
}
We systematically study the moduli theory of singular symplectic varieties which have a resolution by an irreducible symplectic manifold and prove an analog of Verbitsky's global Torelli theorem. In place of twistor lines, Verbitsky's work on ergodic complex structures provides the essential global input. On the one hand, our deformation theoretic results are a further generalization of Huybrechts' theorem on deformation equivalence of birational hyperkahler manifolds to the context of singular… 
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