A Fourier transform for sheaves on Lagrangian families of real tori

Abstract

We systematically develop a transform of the Fourier-Mukai type for sheaves on symplectic manifolds $X$ of any dimension fibred in Lagrangian tori. One obtains a bijective correspondence between unitary local systems supported on Lagrangian submanifolds of $X$ and holomorphic vector bundles with compatible unitary connections supported on complex submanifolds of the relative Jacobian of $X$ (suitable conditions being verified on both sides).

Latex, 30 pages (in a4wide format), no figures. v2: Minor expository changes, typos corrected. v3: Final version to appear in two parts in J. Geom. Phys

References in corpus (1)

• Fourier-Mukai Transform and Mirror Symmetry for D-Branes on Elliptic Calabi-Yau

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• Homological mirror symmetry and Fourier-Mukai transform