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A Fourier transform for sheaves on real tori: Part II. Relative theory

✍ Scribed by U. Bruzzo; G. Marelli; F. Pioli

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 138 KB
Volume: 41
Category: Article
ISSN: 0393-0440
DOI: 10.1016/s0393-0440(01)00065-1

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✦ Synopsis

If X is a symplectic family of Lagrangian tori, the dual family 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 X (suitable conditions being verified on both sides).

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✍ U. Bruzzo; G. Marelli; F. Pioli 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 96 KB

As a first step toward a theory of a real Fourier transform for sheaves on Calabi-Yau manifolds fibred in special Lagrangian tori, we explicitly construct the functors which establish the equivalence between the category of skyscraper sheaves of finite-dimensional vector spaces on a real torus T , a