Details
Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics
Progress in Mathematics, Band 276
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181,89 € |
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| Verlag: | Birkhäuser |
| Format: | |
| Veröffentl.: | 12.06.2009 |
| ISBN/EAN: | 9780817646639 |
| Sprache: | englisch |
| Anzahl Seiten: | 418 |
Dieses eBook enthält ein Wasserzeichen.
Beschreibungen
<P>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.</P>
<P>"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.</P>
<P>Key features: Basic constructions and definitions are presented in preliminary background chapters - Presentation explores applications and suggests several open questions - Extensive bibliography and index.</P>
<P>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.</P>
<P>"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.</P>
<P>Key features: Basic constructions and definitions are presented in preliminary background chapters - Presentation explores applications and suggests several open questions - Extensive bibliography and index.</P>
<P>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.</P>
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.
<P>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.</P>
<P><EM>Fourier–Mukai and Nahm Transforms in Geometry and Mathematical Physics</EM> 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.</P>
<P>Key features:</P>
<P>* Basic constructions and definitions are presented in preliminary background chapters</P>
<P>* Presentation explores applications and suggests several open questions</P>
<P>* Extensive bibliography and index</P>
<P>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.</P>
<P><EM>Fourier–Mukai and Nahm Transforms in Geometry and Mathematical Physics</EM> 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.</P>
<P>Key features:</P>
<P>* Basic constructions and definitions are presented in preliminary background chapters</P>
<P>* Presentation explores applications and suggests several open questions</P>
<P>* Extensive bibliography and index</P>
<P>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.</P>
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
Integral transforms, such as the Laplace and Fourier transforms, have
been major tools in mathematical physics for at least two centuries.
This book 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. The book provides an introduction to current research in
mathematical physics and is particularly useful to graduate students
or researchers just entering this field.
been major tools in mathematical physics for at least two centuries.
This book 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. The book provides an introduction to current research in
mathematical physics and is particularly useful to graduate students
or researchers just entering this field.
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