A Fourier transform for sheaves on Lagrangian families of real tori

Details A Fourier transform for sheaves on Lagrangian families of real tori A Fourier transform for sheaves on Lagrangian families of real tori

2001-05-24

arxiv.org/abs/math/0105196v3

J. Geom. Phys. 39 (2001) 174-182; J. Geom. Phys. 41 (2002) 312-329

Mathematics

Differential Geometry

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

Scientific paper

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).

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