Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics

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.

• Fourier-Mukai partners
• Gauge theory
• Integral functors
• Nahm transforms
• Stability conditions
• birational geometry
• mathematical physics
• partial differential equations

From the reviews:

“The main aim of the book under review is to study a class of functors between derived categories of coherent sheaves of smooth varieties, known as integral (or, in some cases, Fourier-Mukai) functors. Recently, this subject is rapidly developing and the book under review contains a valuable survey of the known results. … the book is very well written and it will certainly be very useful to researchers in algebraic geometry and mathematical physics.” (Adrian Langer, Zentralblatt MATH, Vol. 1186, 2010)

“The monograph under review surveys the developments in the subject since Mukai’s original discovery, mainly concentrating on geometric aspects. … the authors do a good job of being precise while at the same time remaining readable. … there are appendices on background material, including triangulated categories, as well as a final outlook section on stability conditions, making the presentation self-contained and also largely complete in terms of recent developments. … more accessible to graduate students and working mathematicians … .”­­­ (Balázs Szendrői, Mathematical Reviews, Issue 2010 k)

• Dipto. Matematica, Università Genova, Genova, Italy

  Claudio Bartocci

• Studi Avanzati (SISSA), Scuola Internazionale Superiore di, Trieste, Italy

  Ugo Bruzzo

• Fac. Ciencias, Universidad Salamanca, Salamanca, Spain

  Daniel Hernández Ruipérez

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