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  3. Cohomology of Vector Bundles and Syzygies
  • Cited by 198
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    • Publisher:
      Cambridge University Press
      Publication date:
      18 August 2009
      09 June 2003
      ISBN:
      9780511546556
      9780521621977
      DOI:
      https://doi.org/10.1017/CBO9780511546556
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.73kg, 384 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Geometry and Topology, Algebra
      Series:
      Cambridge Tracts in Mathematics (149)
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    Subjects:
    Mathematics (general), Mathematics, Geometry and Topology, Algebra
    Series:
    Cambridge Tracts in Mathematics (149)
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    Book 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 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.

    Reviews

    ' … read this book … instantly became the standard reference …'

    Source: Zentralblatt MATH

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