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Fourier Mukai Transforms and Applications to String Theory

Bjorn Andreas·Daniel Hernandez Ruiperez
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Abstract

We give an introductory review of Fourier-Mukai transforms and their application to various aspects of moduli problems, string theory and mirror symmetry. We develop the necessary mathematical background for Fourier-Mukai transforms such as aspects of derived categories and integral functors as well as their relative version which becomes important for making precise the notion of fiberwise T-duality on elliptic Calabi-Yau threefolds. We discuss various applications of the Fourier-Mukai transform to D-branes on Calabi-Yau manifolds as well as homological mirror symmetry and the construction of vector bundles for heterotic string theory.

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Bjorn Andreas, Daniel Hernandez Ruiperez. 2005-01-18. Fourier Mukai Transforms and Applications to String Theory. https://arxiv.org/abs/math/0412328

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