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arXiv · 0803.1645

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

Mats Boij·Jonas Soderberg
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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.

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Mats Boij, Jonas Soderberg. 2008-03-11. Betti numbers of graded modules and the Multiplicity Conjecture in the non-Cohen-Macaulay case. https://arxiv.org/abs/0803.1645

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