|
|||||
 |
|
|
|
|
|
|
|
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
|
Abstract |
|
We characterize the cone of -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 -equivariant Betti tables of modules over the coordinate ring of matrices, and, dually, cohomology tables of vector bundles on the Grassmannian . 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. |
PDF Access Denied
We have not been able to recognize your IP address
44.220.249.141
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for USD 40.00:
Keywords
Boij–Söderberg theory, Betti table, cohomology table, Schur
functors, Grassmannian, free resolutions, equivariant
K-theory
|
Mathematical Subject Classification 2010
Primary: 13D02
Secondary: 05E99
|
Milestones
Received: 21 August 2016
Revised: 4 December 2017
Accepted: 3 January 2018
Published: 13 May 2018
|
Authors |
| 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 |
|
