Vol. 12, No. 2, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 7, 1221–1401
Issue 6, 1039–1219
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
Editors' interests
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author index
To appear
Other MSP journals
Towards Boij–Söderberg theory for Grassmannians: the case of square matrices

Nicolas Ford, Jake Levinson and Steven V Sam

Vol. 12 (2018), No. 2, 285–303

We characterize the cone of GL-equivariant Betti tables of Cohen–Macaulay modules of codimension 1, up to rational multiple, over the coordinate ring of square matrices. This result serves as the base case for “Boij–Söderberg theory for Grassmannians,” with the goal of characterizing the cones of GLk-equivariant Betti tables of modules over the coordinate ring of k × n matrices, and, dually, cohomology tables of vector bundles on the Grassmannian Gr(k, n). The proof uses Hall’s theorem on perfect matchings in bipartite graphs to compute the extremal rays of the cone, and constructs the corresponding equivariant free resolutions by applying Weyman’s geometric technique to certain graded pure complexes of Eisenbud–Fløystad–Weyman.

Boij–Söderberg theory, Betti table, cohomology table, Schur functors, Grassmannian, free resolutions, equivariant K-theory
Mathematical Subject Classification 2010
Primary: 13D02
Secondary: 05E99
Received: 21 August 2016
Revised: 4 December 2017
Accepted: 3 January 2018
Published: 13 May 2018
Nicolas Ford
Mathematics Department
University of California
Berkeley, CA
United States
Jake Levinson
Mathematics Department
University of Michigan
Ann Arbor, MI
United States
Mathematics Department
University of Washington
Seattle, WA
United States
Steven V Sam
Mathematics Department
University of Wisconsin
Madison, WI
United States