Resolving the Module of Derivations on an n (n+1) Determinantal Ring

We use the construction of the relative bar resolution via differential graded structures to obtain the minimal graded free resolution of Derₑ ₊, where R is a determinantal ring defined by the maximal minors of an n (n+1) generic matrix and k is its coefficient field. Along the way, we compute an explicit action of the Hilbert-Burch differential graded algebra on a differential graded module resolving the cokernel of the Jacobian matrix whose kernel is Derₑ ₊. As a consequence of the minimality of the resulting relative bar resolution, we get a minimal generating set for Derₑ ₊ as an R-module, which, while already known, has not been obtained via our methods.