Abstract
We shall treat five related areas in this chapter:
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1.
Uniqueness of free resolutions
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2.
Fitting ideals of modules
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3.
What makes a complex exact?
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4.
The Hilbert-Burch structure theorem for perfect ideals of codimension 2
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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.
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© 1995 Springer-Verlag New York, Inc.
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Eisenbud, D. (1995). Free Resolutions and Fitting Invariants. In: Commutative Algebra. Graduate Texts in Mathematics, vol 150. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5350-1_22
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DOI: https://doi.org/10.1007/978-1-4612-5350-1_22
Publisher Name: Springer, New York, NY
Print ISBN: 978-3-540-78122-6
Online ISBN: 978-1-4612-5350-1
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