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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by Tran Nam Trung

Proc. Amer. Math. Soc. 137 (2009), 2169-2174

DOI: https://doi.org/10.1090/S0002-9939-09-09640-3

Published electronically: February 12, 2009

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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.

References

Winfried Bruns and Jürgen Herzog, Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics, vol. 39, Cambridge University Press, Cambridge, 1993. MR 1251956
S. Dale Cutkosky, Jürgen Herzog, and Ngô Viêt Trung, Asymptotic behaviour of the Castelnuovo-Mumford regularity, Compositio Math. 118 (1999), no. 3, 243–261. MR 1711319, DOI 10.1023/A:1001559912258
Lê Tuân Hoa and Eero Hyry, On local cohomology and Hilbert function of powers of ideals, Manuscripta Math. 112 (2003), no. 1, 77–92. MR 2005931, DOI 10.1007/s00229-003-0393-1
Vijay Kodiyalam, Asymptotic behaviour of Castelnuovo-Mumford regularity, Proc. Amer. Math. Soc. 128 (2000), no. 2, 407–411. MR 1621961, DOI 10.1090/S0002-9939-99-05020-0
Richard P. Stanley, Combinatorics and commutative algebra, 2nd ed., Progress in Mathematics, vol. 41, Birkhäuser Boston, Inc., Boston, MA, 1996. MR 1453579
Ngô Viêt Trung and Hsin-Ju Wang, On the asymptotic linearity of Castelnuovo-Mumford regularity, J. Pure Appl. Algebra 201 (2005), no. 1-3, 42–48. MR 2158746, DOI 10.1016/j.jpaa.2004.12.043