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2018 Towards Boij–Söderberg theory for Grassmannians: the case of square matrices
Nicolas Ford, Jake Levinson, Steven V Sam
Algebra Number Theory 12(2): 285-303 (2018). DOI: 10.2140/ant.2018.12.285

Abstract

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.

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Nicolas Ford. Jake Levinson. Steven V Sam. "Towards Boij–Söderberg theory for Grassmannians: the case of square matrices." Algebra Number Theory 12 (2) 285 - 303, 2018. https://doi.org/10.2140/ant.2018.12.285

Information

Received: 21 August 2016; Revised: 4 December 2017; Accepted: 3 January 2018; Published: 2018
First available in Project Euclid: 23 May 2018

zbMATH: 06880889
MathSciNet: MR3803704
Digital Object Identifier: 10.2140/ant.2018.12.285

Subjects:
Primary: 13D02
Secondary: 05E99

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.12 • No. 2 • 2018
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