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Fall and Winter 2016 Asymptotic stabilization of Betti diagrams of generic initial systems
Sarah Mayes-Tang
Illinois J. Math. 60(3-4): 845-858 (Fall and Winter 2016). DOI: 10.1215/ijm/1506067295

Abstract

Several authors investigating the asymptotic behaviour of the Betti diagrams of the graded system $\{I^{k}\}$ independently showed that the shape of the nonzero entries in the diagrams stabilizes when $I$ is a homogeneous ideal with generators of the same degree. In this paper, we study the Betti diagrams of graded systems of ideals built by taking the initial ideals or generic initial ideals of powers, and discuss the stabilization of additional collections of Betti diagrams. Our main result shows that when $I$ has generators of the same degree, the entries in the Betti diagrams of the reverse lexicographic generic initial system $\{\operatorname{gin}(I^{k})\}$ are given asymptotically by polynomials and that the shape of the diagrams stabilizes.

Citation

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Sarah Mayes-Tang. "Asymptotic stabilization of Betti diagrams of generic initial systems." Illinois J. Math. 60 (3-4) 845 - 858, Fall and Winter 2016. https://doi.org/10.1215/ijm/1506067295

Information

Received: 3 December 2016; Revised: 1 July 2017; Published: Fall and Winter 2016
First available in Project Euclid: 22 September 2017

zbMATH: 06790331
MathSciNet: MR3705448
Digital Object Identifier: 10.1215/ijm/1506067295

Subjects:
Primary: 13D02, 13P10

Rights: Copyright © 2016 University of Illinois at Urbana-Champaign

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Vol.60 • No. 3-4 • Fall and Winter 2016
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