Overview
- Provides an expository account of Fourier–Mukai and Nahm Transforms
- Includes recent developments for which no thorough account exists
- Includes supplementary material: sn.pub/extras
Part of the book series: Progress in Mathematics (PM, volume 276)
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Table of contents (11 chapters)
Keywords
About this book
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.
Reviews
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)
Authors and Affiliations
Bibliographic Information
Book Title: Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics
Authors: Claudio Bartocci, Ugo Bruzzo, Daniel Hernández Ruipérez
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/b11801
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Boston 2009
Hardcover ISBN: 978-0-8176-3246-5Published: 04 June 2009
eBook ISBN: 978-0-8176-4663-9Published: 12 June 2009
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: XVI, 418
Number of Illustrations: 83 b/w illustrations
Topics: Physics, general, Algebraic Geometry, Partial Differential Equations, Differential Geometry, Theoretical, Mathematical and Computational Physics