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

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.

arXiv comment14 pages

References in corpus (2)

• Betti Numbers of Graded Modules and Cohomology of Vector Bundles
• Bounds for Hilbert coefficients

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• Level algebras through Buchsbaum* manifolds