Virtual criterion for generalized Eagon-Northcott complexes
Caitlyn Booms-Peot, John Cobb
TL;DR
This paper establishes a new criterion for when generalized Eagon-Northcott complexes, associated with maps of free modules, serve as virtual resolutions, expanding the class of known virtual resolutions beyond minimal free resolutions.
Contribution
It provides a sufficient criterion for generalized Eagon-Northcott complexes to be virtual resolutions, including examples not arising from minimal free resolutions.
Findings
Identifies conditions under which these complexes are virtual resolutions
Expands the known classes of virtual resolutions
Includes examples beyond minimal free resolutions
Abstract
Given any map of finitely generated free modules, Buchsbaum and Eisenbud define a family of generalized Eagon-Northcott complexes associated to it. We give sufficient criterion for these complexes to be virtual resolutions, thus adding to the known examples of virtual resolutions, particularly those not coming from minimal free resolutions.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Operator Algebra Research