Subcomplexes of Certain Free Resolutions

Abstract

We invoke the Bernstein–Gel $'$ fand–Gel $'$ fand (BGG) correspondence to study subcomplexes of free resolutions given by two well-known complexes, the Koszul and the Eagon–Northcott. This approach provides a complete characterization of the ranks of free modules in a subcomplex in the Koszul case and imposes numerical restrictions in the Eagon–Northcott case.