Fourier Mukai Transforms and Applications to String Theory

Details Fourier Mukai Transforms and Applications to String Theory Fourier Mukai Transforms and Applications to String Theory

2004-12-16

arxiv.org/abs/math/0412328v2

Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat, 99 (1) (2005) 29-77

Mathematics

Algebraic Geometry

52 pages. To appear in Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. Minor changes, reference of conjecture in section 7.

Scientific paper

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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