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Complex Lagrangians in a hyperKähler manifold and the relative Albanese

Complex Manifolds


<jats:title>Abstract</jats:title><jats:p>Let <jats:italic>M</jats:italic> be the moduli space of complex Lagrangian submanifolds of a hyperKähler manifold <jats:italic>X</jats:italic>, and let ω̄ : 𝒜̂ → <jats:italic>M</jats:italic> be the relative Albanese over <jats:italic>M</jats:italic>. 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 <jats:italic>M</jats:italic>.</jats:p>

Indranil Biswas

Tomás Gómez


Year of publication: 2020

Volume: 7

Issue: 1

Pages: 230--240


ISSN: 2300-7443

Alternative Titles