Combinatorial Interpretations of some Boij-Söderberg Decompositions

Details Combinatorial Interpretations of some Boij-Söderberg Decompositions Combinatorial Interpretations of some Boij-Söderberg Decompositions

2012-03-29

arxiv.org/abs/1203.6515v1

Mathematics

Commutative Algebra

18 pages, 3 figures

Scientific paper

Boij-S\"oderberg theory shows that the Betti table of a graded module can be written as a liner combination of pure diagrams with integer coefficients. Using Ferrers hypergraphs and simplicial polytopes, we provide interpretations of these coefficients for ideals with a d-linear resolution, their quotient rings, and for Gorenstein rings whose resolution has essentially at most two linear strands. We also establish a structural result on the decomposition in the case of quasi-Gorenstein modules.

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