Abstract
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.
Citation
Mats Boij. Jonas Söderberg. "Betti numbers of graded modules and the multiplicity conjecture in the non-Cohen–Macaulay case." Algebra Number Theory 6 (3) 437 - 454, 2012. https://doi.org/10.2140/ant.2012.6.437
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