Claudio Bartocci, Ugo Bruzzo, Daniel Hernández Ruipérez

Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 418
• Erscheinungstermin: 12. Juni 2009
• Englisch
• ISBN-13: 9780817646639
• Artikelnr.: 37338604

Inhaltsangabe

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.

Rezensionen

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 Szendröi, Mathematical Reviews, Issue 2010 k)