Free Resolutions and Fitting Invariants

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


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.


Exact Sequence Local Ring Free Resolution Twisted Section Minimal Free Resolution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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