Vol. 6, No. 3, 2012

Download this article
Download this article For screen
For printing
Recent Issues

Volume 16
Issue 2, 231–519
Issue 1, 1–230

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
Betti numbers of graded modules and the multiplicity conjecture in the non-Cohen–Macaulay case

Mats Boij and Jonas Söderberg

Vol. 6 (2012), No. 3, 437–454

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.

graded modules, Betti numbers, multiplicity conjecture
Mathematical Subject Classification 2000
Primary: 13D02
Secondary: 13A02
Received: 2 July 2010
Revised: 24 January 2011
Accepted: 23 May 2011
Published: 5 July 2012
Mats Boij
Department of Mathematics
SE-100 44 Stockholm
Jonas Söderberg
Department of Mathematics
SE-100 44 Stockholm