Regularity and linearity defect of modules over local rings

2013/09/18 by Maleki, Rasoul Ahangari, Rossi, Maria Evelina
#13D02 #13D07 #16S37 #16W50 #16W70 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1309.4538

Abstract

Given a finitely generated module M over a commutative local ring (or a standard graded k-algebra) (R,\m,k) we detect its complexity in terms of numerical invariants coming from suitable \m-stable filtrations \mathbbM on M. We study the Castelnuovo-Mumford regularity of gr_\mathbbM(M) and the linearity defect of M, denoted \ld_R(M), through a deep investigation based on the theory of standard bases. If M is a graded R-module, then \reg_R(gr_\mathbbM(M))

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