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The global moduli theory of symplectic varieties
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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 $b_2\geq 5$) which does not use the existence of a hyperk\"ahler metric or twistor deformations.
Forward citations
Cited by 3 Pith papers
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Integral cohomology of quotients via toric geometry
A toric blow-up method computes the integral cohomology of quotients by cyclic prime-order groups and yields new Beauville-Bogomolov lattices for K3[m]-type quotients by order 5 and 7 symmetries.
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Mapping class group and global Torelli theorem for hyperkahler manifolds: an erratum
Corrected proofs for the global Torelli theorem for hyperkähler manifolds are supplied by switching from the Teichmüller space to the marked moduli space and by adding an ergodic lemma on lattice isometry groups.
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Deformations and BBF form on non-Kahler holomorphically symplectic manifolds
Bogomolov-Guan manifolds have unobstructed holomorphically symplectic deformations and admit a Beauville-Bogomolov-Fujiki form satisfying the Fujiki formula.
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