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Foundations of Boij-Söderberg Theory for Grassmannians

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Author(s): Jake Levinson
Series: PhD Thesis
Publisher: University of Michigan
Year: 2017

Language: English

Acknowledgments
Table of Contents
List of Appendices
Abstract
Syzygies and Boij-Söderberg theory
Goals of this thesis
What are syzygies?
Boij-Söderberg theory for graded modules
Grassmannian Boij-Söderberg theory
Results of this thesis
Preliminaries
Spaces of interest
Representation theory of the general linear group
Equivariant rings, modules and syzygies
The base case: square matrices
Results on the cones k,k and Dk,k
Constructing Pure Resolutions
The general case: rectangular matrices
The equivariant Herzog-Kühl equations
The pairing between Betti tables and cohomology tables
Appendices
Local cohomology and sheaf cohomology for Grassmannians
Local and sheaf cohomology for graded modules
Local and sheaf cohomology for equivariant modules
Perfect matchings of infinite-dimensional vector spaces
Bibliography