Complex Lagrangians in a hyperKähler manifold and the relative Albanese

Let be the moduli space of complex Lagrangian submanifolds of a hyperKähler manifold , and let ω̄ : 𝒜̂ → be the relative Albanese over . We prove that 𝒜̂ has a natural holomorphic symplectic structure. The projection ω̄ defines a completely integrable structure on the symplectic manifold 𝒜̂. In part...

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Published inComplex manifolds (Warsaw, Poland) Vol. 7; no. 1; pp. 230 - 240
Main Authors Biswas, Indranil, Gómez, Tomás L., Oliveira, André
Format Journal Article
LanguageEnglish
Published De Gruyter 27.10.2020
Subjects
14D21
14J42
37K10
53D12
Albanese
complex Lagrangian
HyperKähler manifold
integrable system
Liouville form
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Summary:Let be the moduli space of complex Lagrangian submanifolds of a hyperKähler manifold , and let ω̄ : 𝒜̂ → be the relative Albanese over . 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
ISSN:2300-7443
2300-7443
DOI:10.1515/coma-2020-0106