Cohomology of vector bundles and syzygies

By:

Weyman, Jerzy

Series: Cambridge tracts in mathematics, no. 149Publication details: Cambridge University Press, 2003. New York:Description: xiv, 368p.; hbk; 24cmISBN:

9780521621977

Subject(s):

DDC classification:

512.5 WEY

Summary: The central theme of this book is an exposition of the geometric technique of calculating syzygies. It is written from a point of view of commutative algebra, and without assuming any knowledge of representation theory the calculation of syzygies of determinantal varieties is explained. The starting point is a definition of Schur functors, and these are discussed from both an algebraic and geometric point of view. Then a chapter on various versions of Bott's Theorem leads on to a careful explanation of the technique itself, based on a description of the direct image of a Koszul complex. Applications to determinantal varieties follow, plus there are also chapters on applications of the technique to rank varieties for symmetric and skew symmetric tensors of arbitrary degree, closures of conjugacy classes of nilpotent matrices, discriminants and resultants. Numerous exercises are included to give the reader insight into how to apply this important method. https://www.cambridge.org/core/books/cohomology-of-vector-bundles-and-syzygies/CBC929779F70722D5D67ACDCE5970087#fndtn-information

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar	General	512.5 WEY (Browse shelf(Opens below))	1	Available		031765

Includes index and references

The central theme of this book is an exposition of the geometric technique of calculating syzygies. It is written from a point of view of commutative algebra, and without assuming any knowledge of representation theory the calculation of syzygies of determinantal varieties is explained. The starting point is a definition of Schur functors, and these are discussed from both an algebraic and geometric point of view. Then a chapter on various versions of Bott's Theorem leads on to a careful explanation of the technique itself, based on a description of the direct image of a Koszul complex. Applications to determinantal varieties follow, plus there are also chapters on applications of the technique to rank varieties for symmetric and skew symmetric tensors of arbitrary degree, closures of conjugacy classes of nilpotent matrices, discriminants and resultants. Numerous exercises are included to give the reader insight into how to apply this important method.

https://www.cambridge.org/core/books/cohomology-of-vector-bundles-and-syzygies/CBC929779F70722D5D67ACDCE5970087#fndtn-information

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