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BY 4.0 license Open Access Published by De Gruyter Open Access October 27, 2020

Complex Lagrangians in a hyperKähler manifold and the relative Albanese

  • Indranil Biswas EMAIL logo , Tomás L. Gómez and André Oliveira
From the journal Complex Manifolds


Let M be the moduli space of complex Lagrangian submanifolds of a hyperKähler manifold X, and let ω̄ : 𝒜̂ → M be the relative Albanese over M. We prove that 𝒜̂ has a natural holomorphic symplectic structure. The projection ω̄ defines a completely integrable structure on the symplectic manifold 𝒜̂. In particular, the fibers of ω̄ are complex Lagrangians with respect to the symplectic form on 𝒜̂. We also prove analogous results for the relative Picard over M.

MSC 2010: 14J42; 53D12; 37K10; 14D21


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Received: 2020-06-29
Accepted: 2020-10-18
Published Online: 2020-10-27

© 2020 Indranil Biswas et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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