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Koszul Algebras and Regularity

  • Aldo Conca
  • Emanuela De Negri
  • Maria Evelina Rossi
Chapter

Abstract

This is a survey paper on commutative Koszul algebras and Castelnuovo-Mumford regularity. Koszul algebras, originally introduced by Priddy, are graded K-algebras R whose residue field K has a linear free resolution as an R-module. The Castelnuovo-Mumford regularity is, after Krull dimension and multiplicity, perhaps the most important invariant of a finitely generated graded module M, as it controls the vanishing of both syzygies and the local cohomology modules of M.

Keywords

Polynomial Ring Hilbert Series Free Resolution Residue Field Linear Defect 
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.

Notes

Acknowledgements

We thank Rasoul Ahangari, Lucho Avramov, Giulio Caviglia, Ralf Fröberg, Jüergen Herzog, Srikanth Iyengar, Liana Şega, Bart Snapp, Rekha Thomas and Matteo Varbaro for useful discussion concerning the material presented in this chapter.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Aldo Conca
    • 1
  • Emanuela De Negri
    • 1
  • Maria Evelina Rossi
    • 1
  1. 1.Dipartimento di MatematicaUniversità degli Studi di GenovaGenovaItaly

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