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A Fourier transform for sheaves on real tori. II: Relative theory. (English) Zbl 1071.14515
Summary: If $$X$$ is a symplectic family of Lagrangian tori, the dual family $$\widehat X$$ has a natural complex structure. We define, for any dimension of $$X$$, a Fourier transform which yields a bijective correspondence between local systems supported on Lagrangian submanifolds of $$X$$ and holomorphic vector bundles supported on complex subvarieties of $$\widehat X$$ (suitable conditions being verified on both sides).

##### MSC:
 14J32 Calabi-Yau manifolds (algebro-geometric aspects) 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results 32Q25 Calabi-Yau theory (complex-analytic aspects) 58J22 Exotic index theories on manifolds
##### Keywords:
Strominger-Yau-Zaslow conjecture
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##### References:
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