A global Torelli theorem for singular symplectic varieties

By Benjamin Bakker, C. Lehn. 2016

53 citations recorded by the source corpus.

We systematically study the moduli theory of singular symplectic varieties which have a resolution by an irreducible symplectic manifold and prove an analog of Verbitsky's global Torelli theorem. In place of twistor lines, Verbitsky's work on ergodic complex structures provides the essential global input. On the one hand, our deformation theoretic results are a further generalization of Huybrechts' theorem on deformation equivalence of birational hyperkahler manifolds to the context of singular symplectic varieties. On the other hand, our global moduli theory provides a framework for understanding and classifying the symplectic singularities that arise from birational contractions of irreducible symplectic manifolds, and there are a number of applications to $K3^{[n]}$-type varieties.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/52a939269c2d719f32c2b1c1c005d6fb409ea5cb

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In Geometry and Topology

1. Yoshiki Oshima
2. Y. Odaka
3. Robert J. Berman
4. R. Dervan
5. Chenyang Xu
6. Chi Li
7. Song Sun
8. Mattias Jonsson

In Mathematical Physics

1. Yoshiki Oshima
2. Y. Odaka
3. Chi Li
4. Song Sun
5. Robert J. Berman
6. R. Dervan
7. Cristiano Spotti
8. S. Boucksom

Citations in the corpus

• Collapsing K3 Surfaces, Tropical Geometry and Moduli Compactifications of Satake, Morgan-Shalen Type (2018, background): “thor had a chance to attend Christian Lehn’s talk. There the first author learnt that Benjamin Bakker and he seem to have also somewhat similar arguments to prove different statements (cf., [BL], also [BL16] written before), which studies the locus along equisingular deformation in the moduli. 145 ap”