Abstract
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. 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.
Original language | English |
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Pages (from-to) | 54-72 |
Number of pages | 19 |
Journal | Journal of Algebra |
Volume | 381 |
DOIs | |
State | Published - May 1 2013 |
Bibliographical note
Funding Information:✩ This work was partially supported by a grant from the Simons Foundation (#208869 to Uwe Nagel) and by the National Security Agency under Grant No. H98230-12-1-0247. The second author also would like to thank MSRI for organizing and funding the summer workshop on commutative algebra in 2011 as well as Daniel Erman for his inspiring lectures. * Corresponding author. E-mail addresses: uwe.nagel@uky.edu (U. Nagel), stephen.sturgeon@uky.edu (S. Sturgeon).
Keywords
- Boij-Söderberg theory
- Ferrers hypergraph
- Gorenstein ring
- Linear resolution
- O-sequence
- Quasi-Gorenstein module
ASJC Scopus subject areas
- Algebra and Number Theory