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A Fourier transform for sheaves on real tori: Part I. The equivalence Sky(T)≃ Loc(T̂)

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

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 96 KB
Volume: 39
Category: Article
ISSN: 0393-0440
DOI: 10.1016/s0393-0440(01)00009-2

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✦ Synopsis

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 , and the category of local systems (locally free sheaves of C-modules of finite rank) on the dual torus T .

📜 SIMILAR VOLUMES

A Fourier transform for sheaves on real

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

✍ U. Bruzzo; G. Marelli; F. Pioli 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 138 KB

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 o