BARTOCCI, CLAUDIO, Bruzzo, Ugo, Hernández Ruipérez, Daniel
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Provides an expository account of Fourier–Mukai and Nahm Transforms
Includes recent developments for which no thorough account exists
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.
* 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.
Content Level »Research
Keywords »Fourier-Mukai partners - Gauge theory - Integral functors - Nahm transforms - Stability conditions - birational geometry - mathematical physics