Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics

Inbunden, Engelska, 2009

Av CLAUDIO BARTOCCI, Ugo Bruzzo, Daniel Hernández Ruipérez, Claudio Bartocci

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Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematical physics for at least two centuries. In the last 25 years, the development of gauge theory has been closely related to new generalizations of integral transforms of a more geometric character. "Nahm and Fourier--Mukai Transforms in Geometry and Mathematical Physics" examines the differential-geometric constructions (Nahm) as well as the algebro-geometric approach (Fourier--Mukai functors). Also included is a considerable amount of material scattered in the literature and not systematically organized in any existing textbook or monograph. Key features: * Basic constructions and definitions are presented in preliminary background chapters so that the work is self-contained * Applications are presented * Open questions for graduate students and researchers * Good bibliography and index The book provides an introduction to current research in mathematical physics and is particularly useful to graduate students or researchers just entering this field.

Produktinformation

Utgivningsdatum2009-06-04
Mått155 x 235 x 25 mm
Vikt789 g
FormatInbunden
SpråkEngelska
SerieProgress in Mathematics
Antal sidor418
Upplaga2009
FörlagBirkhauser Boston Inc
ISBN9780817632465

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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 ... ."--- (Balazs Szendroi, Mathematical Reviews, Issue 2010 k)