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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).

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
Full Text: DOI arXiv
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