Cohomology of vector bundles and syzygies
Series: Cambridge tracts in mathematics, no. 149Publication details: Cambridge University Press, 2003. New York:Description: xiv, 368p.; hbk; 24cmISBN:- 9780521621977
- 512.5 WEY
Item type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode |
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Books | IIT Gandhinagar | General | 512.5 WEY (Browse shelf(Opens below)) | 1 | Available | 031765 |
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512.5 SUN Numerical linear algebra | 512.5 TRE Numerical linear algebra | 512.5 TRE Numerical linear algebra | 512.5 WEY Cohomology of vector bundles and syzygies | 512.50285 CUL Introduction to numerical linear algebra | 512.523 HAL Finite-dimensional vector spaces | 512.523 HAL Finite-dimensional vector spaces |
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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