Fourier-Mukai and Nahm transforms in geometry and mathematical physics

Claudio Bartocci, Ugo Bruzzo, Daniel Hernández Ruipérez (auth.)0817632468, 9780817632465, 9780817646639

Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries. In the last three decades the development of a number of novel ideas in algebraic geometry, category theory, gauge theory, and string theory has been closely related to generalizations of integral transforms of a more geometric character.

Fourier–Mukai and Nahm Transforms in Geometry and Mathematical Physics examines the algebro-geometric approach (Fourier–Mukai functors) as well as the differential-geometric constructions (Nahm). Also included is a considerable amount of material from existing literature which has not been systematically organized into a monograph.

Key features:

* Basic constructions and definitions are presented in preliminary background chapters

* Presentation explores applications and suggests several open questions

* Extensive bibliography and index

This self-contained monograph provides an introduction to current research in geometry and mathematical physics and is intended for graduate students and researchers just entering this field.

Table of contents :
Front Matter….Pages 1-16
Integral functors….Pages 1-30
Fourier-Mukai functors….Pages 31-79
Fourier-Mukai on Abelian varieties….Pages 81-109
Fourier-Mukai on K3 surfaces….Pages 111-146
Nahm transforms….Pages 147-182
Relative Fourier-Mukai functors….Pages 183-232
Fourier-Mukai partners and birational geometry….Pages 233-280
Derived and triangulated categories….Pages 281-337
Lattices….Pages 339-345
Miscellaneous results….Pages 347-358
Stability conditions for derived categories….Pages 359-395
Back Matter….Pages 1-27