Cohomology of Vector Bundles and Syzygies

ISBN-10: 0521621976
ISBN-13: 9780521621977
Edition: 2003
List price: $149.99 Buy it from $139.71
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Description: 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  More...

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Book details

List price: $149.99
Copyright year: 2003
Publisher: Cambridge University Press
Publication date: 6/9/2003
Binding: Hardcover
Pages: 384
Size: 6.25" wide x 9.00" long x 1.25" tall
Weight: 1.496
Language: English

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.

Introduction
Schur functions and Schur complexes
Grassmannians and flag varieties
Bott's theorem
The geometric technique
The determinantal varieties
Higher rank varieties
The nilpotent orbit closures
Resultants and discriminants

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