Regularity index of Hilbert functions of powers of ideals

Trung, Tran

doi:10.1090/S0002-9939-09-09640-3

Regularity index of Hilbert functions of powers of ideals
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Proc. Amer. Math. Soc. 137 (2009), 2169-2174 Request permission

Abstract:

Let $I$ be a homogeneous ideal of a Noetherian standard graded algebra $A$ over an Artinian ring $A_0$, and let $M$ be a finitely generated graded $A$-module. It is shown that the regularity index of the Hilbert function of $I^nM$ is a linear function of $n$ for all $n$ large enough.

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