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SPRING 2014 Stabilization of Betti tables
Gwyneth Whieldon
J. Commut. Algebra 6(1): 113-126 (SPRING 2014). DOI: 10.1216/JCA-2014-6-1-113

Abstract

Let $I\subseteq R=\kk[x_1,\ldots,x_n]$ be a homogeneous ideal generated by forms of degree~$r$. We show here that the shapes of the Betti tables of the ideals $I^d$ stabilize, in the sense that there exists some $D$ such that for all $d\geq D$, $\b_{i,j+rd}(I^d)\neq 0\Leftrightarrow \b_{i,j+rD}(I^D)\neq 0$. We also produce upper bounds for the stabilization index $\text{Stab\,}(I)$. This strengthens the result of Cutkosky, Herzog and Trung that the Castelnuovo-Mumford regularity $\text{reg\,}(I^d)$ is eventually a linear function in $d$.

Citation

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Gwyneth Whieldon. "Stabilization of Betti tables." J. Commut. Algebra 6 (1) 113 - 126, SPRING 2014. https://doi.org/10.1216/JCA-2014-6-1-113

Information

Published: SPRING 2014
First available in Project Euclid: 2 June 2014

zbMATH: 1298.13002
MathSciNet: MR3215565
Digital Object Identifier: 10.1216/JCA-2014-6-1-113

Subjects:
Primary: 13A02, 13C99, 13D02

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

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Vol.6 • No. 1 • SPRING 2014
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