The global moduli theory of symplectic varieties

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 $b_2\ge 5$) which does not use the existence of a hyperkähler metric or twistor deformations.

Minor corrections. Final version, to appear in J. Reine Angew. Math

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Cited by in corpus (16)

• Mapping class group and global Torelli theorem for hyperkahler manifolds: an erratum
• On the monodromy group of desingularised moduli spaces of sheaves on K3 surfaces
• Finiteness for self-dual classes in integral variations of Hodge structure
• On the Betti numbers of compact holomorphic symplectic orbifolds of dimension four
• Integral cohomology of quotients via toric geometry
• Numerical characterization of complex torus quotients
• Motivic integration and the birational invariance of BCOV invariants
• Equality in the Miyaoka-Yau inequality and uniformization of non-positively curved klt pairs
• The second integral cohomology of moduli spaces of sheaves on K3 and Abelian surfaces
• The dual Lagrangian fibration of known hyper-Kähler manifolds
• The Kodaira problem for Kähler spaces with vanishing first Chern class
• Deformations and BBF form on non-Kahler holomorphically symplectic manifolds
• Projective models of Nikulin orbifolds
• On the Kähler cone of irreducible symplectic orbifolds
• On the GHKS compactification of the moduli space of K3 surfaces of degree two
• A decomposition theorem for singular Kähler spaces with trivial first Chern class of dimension at most four