On the asymptotic linearity of Castelnuovo-Mumford regularity

Details On the asymptotic linearity of Castelnuovo-Mumford regularity On the asymptotic linearity of Castelnuovo-Mumford regularity

2002-12-11

arxiv.org/abs/math/0212161v1

Mathematics

Commutative Algebra

7 pages

Scientific paper

Let R be a standard graded ring over a commutative Noetherian ring with unity
and I a graded ideal of R. Let M be a finitely generated graded R-module. We
prove that there exist integers e and \rho_M(I) such that for all large n,
reg(I^nM)= \rho_M(I)n+e.

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