The global moduli theory of symplectic varieties

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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:msub><m:mi>b</m:mi><m:mn>2</m:mn></m:msub><m:mo>≥</m:mo><m:mn>5</m:mn></m:mrow></m:math> {b₂≥ 5} ) which does not use the existence of a hyperkähler metric or twistor deformations.