The global moduli theory of symplectic varieties

By Benjamin Bakker, C. Lehn. Journal für die Reine und Angewandte Mathematik, 2018

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Abstract We develop the global moduli theory of symplectic varieties in the sense of Beauville. We prove a number of analogs of classical results from the smooth case, including a global Torelli theorem. In particular, this yields a new proof of Verbitsky’s global Torelli theorem in the smooth case (assuming b 2 ≥ 5 {b_{2}\geq 5} ) which does not use the existence of a hyperkähler metric or twistor deformations.

Subfields: Geometry and Topology, Mathematical Physics

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