Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics [electronic resource] / by Claudio Bartocci, Ugo Bruzzo, Daniel Hernández Ruipérez.

By: Bartocci, Claudio [author.]
Contributor(s): Bruzzo, Ugo [author.] | Hernández Ruipérez, Daniel [author.] | SpringerLink (Online service)
Material type: TextTextSeries: Progress in Mathematics: 276Publisher: Boston : Birkhäuser Boston, 2009Description: XVI, 418 p. 83 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780817646639Subject(s): Physics | Algebraic geometry | Partial differential equations | Differential geometry | Physics | Physics, general | Algebraic Geometry | Partial Differential Equations | Differential Geometry | Theoretical, Mathematical and Computational PhysicsAdditional physical formats: Printed edition:: No titleDDC classification: 530 LOC classification: QC1-75Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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.
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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.

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.

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