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18 January 2022
 
  » arxiv » 2010.06483

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Complex Lagrangians in a hyperKaehler manifold and the relative Albanese
Indranil Biswas ; Tomás L. Gómez ; André Oliveira ;
Date 13 Oct 2020
AbstractLet $M$ be the moduli space of complex Lagrangian submanifolds of a hyperKähler manifold $X$, and let $varpi : widehat{mathcal{A}} ightarrow M$ be the relative Albanese over $M$. We prove that $widehat{mathcal{A}}$ has a natural holomorphic symplectic structure. The projection $varpi$ defines a completely integrable structure on the symplectic manifold $widehat{mathcal{A}}$. In particular, the fibers of $varpi$ are complex Lagrangians with respect to the symplectic form on $widehat{mathcal{A}}$. We also prove analogous results for the relative Picard over $M$.
Source arXiv, 2010.06483
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