Cohomology of vector bundles and syzygies

Jerzy M. Weyman

386 pages, parution le 25/07/2003

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Résumé

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 Material
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

References
Notation index
Subject index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Jerzy M. Weyman
Parution	25/07/2003
Nb. de pages	386
Format	15,7 x 23,3
Couverture	Relié
Poids	685g
Intérieur	Noir et Blanc
EAN13	9780521621977
ISBN13	978-0-521-62197-7