Open Access
Translator Disclaimer
2012 Betti numbers of graded modules and the multiplicity conjecture in the non-Cohen–Macaulay case
Mats Boij, Jonas Söderberg
Algebra Number Theory 6(3): 437-454 (2012). DOI: 10.2140/ant.2012.6.437

Abstract

We use results of Eisenbud and Schreyer to prove that any Betti diagram of a graded module over a standard graded polynomial ring is a positive linear combination of Betti diagrams of modules with a pure resolution. This implies the multiplicity conjecture of Herzog, Huneke, and Srinivasan for modules that are not necessarily Cohen–Macaulay and also implies a generalized version of these inequalities. We also give a combinatorial proof of the convexity of the simplicial fan spanned by pure diagrams.

Citation

Download Citation

Mats Boij. Jonas Söderberg. "Betti numbers of graded modules and the multiplicity conjecture in the non-Cohen–Macaulay case." Algebra Number Theory 6 (3) 437 - 454, 2012. https://doi.org/10.2140/ant.2012.6.437

Information

Received: 2 July 2010; Revised: 24 January 2011; Accepted: 23 May 2011; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1259.13009
MathSciNet: MR2966705
Digital Object Identifier: 10.2140/ant.2012.6.437

Subjects:
Primary: 13D02
Secondary: 13A02

Keywords: Betti numbers , graded modules , multiplicity conjecture

Rights: Copyright © 2012 Mathematical Sciences Publishers

JOURNAL ARTICLE
18 PAGES


SHARE
Vol.6 • No. 3 • 2012
MSP
Back to Top