Betti numbers of graded modules and the Multiplicity Conjecture in the non-Cohen-Macaulay case
By M. Boij, Jonas Söderberg. 2008
87 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/0588d1fdcd9ed834cdd77a82eb33c6a956a0757f
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In Algebra and Number Theory
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Citations in the corpus
- Free Resolutions and Sparse Determinantal Ideals (2011, background): “In particular, the degrees and ranks of the free modules appearing in a minimal free resolution of (I : x)/I can be no larger than those appearing in F ′ •[1].”