TY  - BOOK
AU  - Bartocci,Claudio
AU  - Bruzzo,Ugo
AU  - Hernández Ruipérez,Daniel
ED  - SpringerLink (Online service)
TI  - Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics
T2  - Progress in Mathematics
SN  - 9780817646639
PY  - 2009///
CY  - Boston
PB  - Birkhäuser Boston
KW  - MATHEMATICS
KW  - GEOMETRY, ALGEBRAIC
KW  - DIFFERENTIAL EQUATIONS, PARTIAL
KW  - GLOBAL DIFFERENTIAL GEOMETRY
KW  - MATHEMATICAL PHYSICS
KW  - ALGEBRAIC GEOMETRY
KW  - PARTIAL DIFFERENTIAL EQUATIONS
KW  - DIFFERENTIAL GEOMETRY
KW  - MATHEMATICAL AND COMPUTATIONAL PHYSICS
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/b11801
ER  -