Betti numbers of graded modules and the Multiplicity Conjecture in the non-Cohen-Macaulay case

Details Betti numbers of graded modules and the Multiplicity Conjecture in the non-Cohen-Macaulay case Betti numbers of graded modules and the Multiplicity Conjecture in the non-Cohen-Macaulay case

2008-03-11

arxiv.org/abs/0803.1645v1

Mathematics

Commutative Algebra

14 pages

Scientific paper

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.

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