The Eagon-Northcott complex of a map of finitely generated free modules has been an interest of study since 1962, as it generically resolves the ideal of maximal minors of the matrix that defines the map. In 1975, Buchsbaum and Eisenbud described a family of generalized Eagon-Northcott complexes associated to a map of free modules, which are also generically minimal free resolutions. As introduced by Berkesch, Erman, and Smith in 2020, when working over a smooth projective toric variety, virtual resolutions, rather than minimal free resolutions, are a better tool for understanding the geometry of a space. I will describe sufficient criteria for the family of generalized Eagon-Northcott complexes of a map to be virtual resolutions, thus adding to the known examples of virtual resolutions, particularly those not coming from minimal free resolutions.
Virtual criterion for generalized Eagon-Northcott complexes
Caitlyn Booms, University of Wisconsin-Madison
Authors: Caitlyn Booms-Peot and John Cobb
2022 AWM Research Symposium
Combinatorial and Homological Methods in Commutative Algebra