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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 | | Abstract: | Let $M$ 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 | | Services: | Forum | Review | PDF | Favorites | |
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