  We study (a generalization of) the notion of linked determinantal loci
recently introduced by the second author, showing that as with classical
determinantal loci, they are Cohen-Macaulay whenever they have the expected
codimension. We apply this to prove Cohen-Macaulayness and flatness for moduli
spaces of limit linear series, and to prove a comparison result between the
scheme structures of Eisenbud-Harris limit linear series and the spaces of
limit linear series recently constructed by the second author. This comparison
result is crucial in order to study the geometry of Brill-Noether loci via
degenerations.
