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The global moduli theory of symplectic varieties

Benjamin Bakker and Christian Lehn ORCID logo EMAIL logo

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

Funding statement: Benjamin Bakker was partially supported by NSF grants DMS-1702149 and DMS-1848049. Christian Lehn was supported by the DFG through the research grants Le 3093/2-1, Le 3093/2-2, and Le 3093/3-1.

Acknowledgements

We benefited from discussions, remarks, emails of Valery Alexeev, Andreas Höring, Daniel Huybrechts, Stefan Kebekus, Manfred Lehn, Thomas Peternell, Antonio Rapagnetta, Bernd Schober, and Christian Schnell. The first named author would like to thank Giulia Saccà for conversations related to Section 7. Both authors are grateful to the referees for a very careful reading and many suggestions that have greatly improved the article.

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Received: 2022-04-18
Published Online: 2022-07-29
Published in Print: 2022-09-01

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