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

References in corpus (18)

• Symplectic singularities
• Differential Forms on Log Canonical Spaces
• Mapping class group and global Torelli theorem for hyperkahler manifolds: an erratum
• A global Torelli theorem for hyperkahler manifolds
• Singular symplectic moduli spaces
• Klt varieties with trivial canonical class -- Holonomy, differential forms, and fundamental groups
• A note on symplectic singularities
• Extending holomorphic forms from the regular locus of a complex space to a resolution of singularities
• Symplectic involutions of holomorphic symplectic fourfolds
• On symplectic automorphisms of hyperkähler fourfolds of K3^[2] type
• Contraction centers in families of hyperkahler manifolds
• Fujiki relations and fibrations of irreducible symplectic varieties
• On deformations of Q-factorial symplectic varieties
• On the Betti numbers of compact holomorphic symplectic orbifolds of dimension four
• A singular Demailly-Paun theorem
• Fujiki relation on symplectic varieties
• Ergodic complex structures on hyperkahler manifolds: an erratum
• Isotrivial elliptic K3 surfaces and Lagrangian fibrations

Cited by in corpus (17)

• 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 existence of universal families of marked irreducible holomorphic symplectic manifolds
• On the Betti numbers of compact holomorphic symplectic orbifolds of dimension four
• Integral cohomology of quotients via toric geometry
• Motivic integration and the birational invariance of BCOV invariants
• Numerical characterization of complex torus quotients
• 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 GHKS compactification of the moduli space of K3 surfaces of degree two
• On the Kähler cone of irreducible symplectic orbifolds
• A decomposition theorem for singular Kähler spaces with trivial first Chern class of dimension at most four