Cohomology of Vector Bundles and Syzygies ebook Weyman, Jerzy Diesel eBooks

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Home > Education > Mathematics > Cohomology of Vector Bundles and Syzygies-eBook

Cohomology of Vector Bundles and Syzygies

Weyman, Jerzy

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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.

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Title of ebook: Cohomology of Vector Bundles and Syzygies
ISBN: 9780511059704
Publisher: Cambridge University Press
Internet download file size: 2683 kb
Pages: 388
Released online for download: 08-13-1999
Author of eBook: Weyman, Jerzy