Algebra & Number Theory
- Algebra Number Theory
- Volume 12, Number 2 (2018), 285-303.
Towards Boij–Söderberg theory for Grassmannians: the case of square matrices
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.
Algebra Number Theory, Volume 12, Number 2 (2018), 285-303.
Received: 21 August 2016
Revised: 4 December 2017
Accepted: 3 January 2018
First available in Project Euclid: 23 May 2018
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Ford, Nicolas; Levinson, Jake; Sam, Steven V. Towards Boij–Söderberg theory for Grassmannians: the case of square matrices. Algebra Number Theory 12 (2018), no. 2, 285--303. doi:10.2140/ant.2018.12.285. https://projecteuclid.org/euclid.ant/1527040845