Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Algebra
Boij-Söderberg Decompositions, Cellular Resolutions, And Polytopes, Stephen Sturgeon
Boij-Söderberg Decompositions, Cellular Resolutions, And Polytopes, Stephen Sturgeon
Theses and Dissertations--Mathematics
Boij-Söderberg theory shows that the Betti table of a graded module can be written as a linear combination of pure diagrams with integer coefficients. In chapter 2 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. These results are published in the Journal of Algebra, see [25].
In chapter 3 we provide some further results about Boij-Söderberg decompositions. We …