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Summer 2010 Betti numbers and shifts in minimal graded free resolutions
Tim Römer
Illinois J. Math. 54(2): 449-467 (Summer 2010). DOI: 10.1215/ijm/1318598667

Abstract

Let $S=K[x_1,\ldots,x_n]$ be a polynomial ring and $R=S/I$ where $I \subset S$ is a graded ideal. The Multiplicity Conjecture of Herzog, Huneke, and Srinivasan which was recently proved using the Boij-Söderberg theory states that the multiplicity of $R$ is bounded above by a function of the maximal shifts in the minimal graded free resolution of $R$ over $S$ as well as bounded below by a function of the minimal shifts if $R$ is Cohen-Macaulay. In this paper, we study the related problem to show that the total Betti-numbers of $R$ are also bounded above by a function of the shifts in the minimal graded free resolution of $R$ as well as bounded below by another function of the shifts if $R$ is Cohen-Macaulay. We also discuss the cases when these bounds are sharp.

Citation

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Tim Römer. "Betti numbers and shifts in minimal graded free resolutions." Illinois J. Math. 54 (2) 449 - 467, Summer 2010. https://doi.org/10.1215/ijm/1318598667

Information

Published: Summer 2010
First available in Project Euclid: 14 October 2011

zbMATH: 1236.05214
MathSciNet: MR2846468
Digital Object Identifier: 10.1215/ijm/1318598667

Subjects:
Primary: 05E99, 13C14, 13D02

Rights: Copyright © 2010 University of Illinois at Urbana-Champaign

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Vol.54 • No. 2 • Summer 2010
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