TY  - GEN
AU  - Weyman, Jerzy
TI  - Cohomology of vector bundles and syzygies
SN  - 9780521621977
U1  - 512.5 
PY  - 2003///
CY  - New York
PB  - Cambridge University Press
KW  - Syzygies
KW  - Mathematics
KW  - Vector bundles
KW  - Homology theory
KW  - Commutative algebra
KW  - Nilpotent matrices
N1  - Includes index and references
N2  - 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
ER  -