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Koszul Algebras and Regularity

In: Commutative Algebra

Author

Listed:
  • Aldo Conca

    (Università degli Studi di Genova, Dipartimento di Matematica)

  • Emanuela De Negri

    (Università degli Studi di Genova, Dipartimento di Matematica)

  • Maria Evelina Rossi

    (Università degli Studi di Genova, Dipartimento di Matematica)

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.

Suggested Citation

  • Aldo Conca & Emanuela De Negri & Maria Evelina Rossi, 2013. "Koszul Algebras and Regularity," Springer Books, in: Irena Peeva (ed.), Commutative Algebra, edition 127, pages 285-315, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-5292-8_8
    DOI: 10.1007/978-1-4614-5292-8_8
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