Betti numbers of graded modules and the Multiplicity Conjecture in the non-Cohen-Macaulay case
Commutative Algebra
2008-03-12 v1 Algebraic Geometry
Abstract
We use the results by Eisenbud and Schreyer to prove that any Betti diagram of a graded module over a standard graded polynomial ring is a positive linear combination 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. We give a combinatorial proof of the convexity of the simplicial fan spanned by the pure diagrams.
Keywords
Cite
@article{arxiv.0803.1645,
title = {Betti numbers of graded modules and the Multiplicity Conjecture in the non-Cohen-Macaulay case},
author = {Mats Boij and Jonas Soderberg},
journal= {arXiv preprint arXiv:0803.1645},
year = {2008}
}
Comments
14 pages