ISBN-10:
0817632468
ISBN-13:
9780817632465
Pub. Date:
06/04/2009
Publisher:
Birkhäuser Boston
Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics / Edition 1

Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics / Edition 1

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Overview

Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics / Edition 1

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.

Product Details

ISBN-13: 9780817632465
Publisher: Birkhäuser Boston
Publication date: 06/04/2009
Series: Progress in Mathematics , #276
Edition description: 2009
Pages: 418
Product dimensions: 6.40(w) x 9.30(h) x 1.20(d)

Table of Contents

Integral functors.- Fourier-Mukai functors.- Fourier-Mukai on Abelian varieties.- Fourier-Mukai on K3 surfaces.- Nahm transforms.- Relative Fourier-Mukai functors.- Fourier-Mukai partners and birational geometry.- Derived and triangulated categories.- Lattices.- Miscellaneous results.- Stability conditions for derived categories.

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