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- W4300501475 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 $mathbb{M}$ on $M$. We study the Castelnuovo-Mumford regularity of $gr_{mathbb{M}}(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 $reg_R(gr_{mathbb{M}}(M)) <infty$ implies $reg_R(M)<infty$ and the converse holds provided $M$ is of homogenous type. An analogous result can be proved in the local case in terms of the linearity defect. Motivated by a positive answer in the graded case, we present for local rings a partial answer to a question raised by Herzog and Iyengar of whether $ld_R(k)<infty$ implies $R$ is Koszul." @default.
- W4300501475 created "2022-10-03" @default.
- W4300501475 creator A5042557616 @default.
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- W4300501475 date "2013-09-18" @default.
- W4300501475 modified "2023-09-28" @default.
- W4300501475 title "Regularity and linearity defect of modules over local rings" @default.
- W4300501475 doi "https://doi.org/10.48550/arxiv.1309.4538" @default.
- W4300501475 hasPublicationYear "2013" @default.
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