Complex Lagrangians in a hyperKähler manifold and the relative Albanese

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. I...

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Autores principales:	Biswas Indranil, Gómez Tomás L., Oliveira André
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2020
Materias:	hyperkähler manifold complex lagrangian integrable system liouville form albanese 14j42 53d12 37k10 14d21 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/0efd9615d33a4299bd832d377f1e7691
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id	oai:doaj.org-article:0efd9615d33a4299bd832d377f1e7691
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spelling	oai:doaj.org-article:0efd9615d33a4299bd832d377f1e76912021-12-02T11:56:24ZComplex Lagrangians in a hyperKähler manifold and the relative Albanese2300-744310.1515/coma-2020-0106https://doaj.org/article/0efd9615d33a4299bd832d377f1e76912020-10-01T00:00:00Zhttp://www.degruyter.com/view/j/coma.2020.7.issue-1/coma-2020-0106/coma-2020-0106.xml?format=INThttps://doaj.org/toc/2300-7443Let 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.Biswas IndranilGómez Tomás L.Oliveira AndréDe Gruyterarticlehyperkähler manifoldcomplex lagrangianintegrable systemliouville formalbanese14j4253d1237k1014d21MathematicsQA1-939ENComplex Manifolds, Vol 7, Iss 1, Pp 230-240 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	hyperkähler manifold complex lagrangian integrable system liouville form albanese 14j42 53d12 37k10 14d21 Mathematics QA1-939
spellingShingle	hyperkähler manifold complex lagrangian integrable system liouville form albanese 14j42 53d12 37k10 14d21 Mathematics QA1-939 Biswas Indranil Gómez Tomás L. Oliveira André Complex Lagrangians in a hyperKähler manifold and the relative Albanese
description	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.
format	article
author	Biswas Indranil Gómez Tomás L. Oliveira André
author_facet	Biswas Indranil Gómez Tomás L. Oliveira André
author_sort	Biswas Indranil
title	Complex Lagrangians in a hyperKähler manifold and the relative Albanese
title_short	Complex Lagrangians in a hyperKähler manifold and the relative Albanese
title_full	Complex Lagrangians in a hyperKähler manifold and the relative Albanese
title_fullStr	Complex Lagrangians in a hyperKähler manifold and the relative Albanese
title_full_unstemmed	Complex Lagrangians in a hyperKähler manifold and the relative Albanese
title_sort	complex lagrangians in a hyperkähler manifold and the relative albanese
publisher	De Gruyter
publishDate	2020
url	https://doaj.org/article/0efd9615d33a4299bd832d377f1e7691
work_keys_str_mv	AT biswasindranil complexlagrangiansinahyperkahlermanifoldandtherelativealbanese AT gomeztomasl complexlagrangiansinahyperkahlermanifoldandtherelativealbanese AT oliveiraandre complexlagrangiansinahyperkahlermanifoldandtherelativealbanese
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Complex Lagrangians in a hyperKähler manifold and the relative Albanese

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