Free Resolutions and Fitting Invariants

  • David Eisenbud
Part of the Graduate Texts in Mathematics book series (GTM, volume 150)

Abstract

We shall treat five related areas in this chapter:
  1. 1.

    Uniqueness of free resolutions

     
  2. 2.

    Fitting ideals of modules

     
  3. 3.

    What makes a complex exact?

     
  4. 4.

    The Hilbert-Burch structure theorem for perfect ideals of codimension 2

     
  5. 5.

    Castelnuovo-Mumford regularity

     
Many invariants in algebraic geometry and commutative algebra—from intersection numbers of varieties to the cohomology of sheaves to the depth and dimension of a module—may be defined in terms of free resolutions. Many of these invariants are actually invariants of the homology of complexes derived from free resolutions. Some others seem accessible only through free resolutions themselves.

Keywords

Lution Reso Eisen 

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Copyright information

© Springer-Verlag New York, Inc. 1995

Authors and Affiliations

  • David Eisenbud
    • 1
  1. 1.Department of MathematicsBrandeis UniversityWalthamUSA

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