A global Torelli theorem for singular symplectic varieties
-- Benjamin Bakker, March 10, 2017

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The local and global deformation theories of holomorphic
symplectic manifolds enjoy many beautiful properties.  By work of
Namikawa, some of the local results generalize to singular symplectic
varieties, but the moduli theory is badly behaved.  In joint work with
C. Lehn we show that for locally trivial deformations the entire
picture is exactly analogous to the smooth case.  In particular, we
prove a global Torelli theorem and deduce some applications to
birational contractions of moduli spaces of vector bundles on K3
surfaces.  In place of twistor lines, the crucial global input is
Verbitsky's work on ergodic complex structures using Ratner's
theorems.