Koszul Algebras and Regularity

Aldo Conca (), Emanuela De Negri () and Maria Evelina Rossi ()
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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

A chapter in Commutative Algebra, 2013, pp 285-315 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-1-4614-5292-8_8

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