A complex that resolves the ideal of minors having $n-1$ columns in common

Abstract:

Let $A$ be an $n \times m$ matrix $(m \geqslant n)$ with entries in a noetherian ring $R$, let $J$ be the ideal of $R$ generated by the $n \times n$ minors that are formed with $n - 1$ fixed columns of $A$. Necessary and sufficient conditions are given in order that a suitably defined complex be a free resolution of the $R$-module $R/J$. The complex is closely related to the complexes of Buchsbaum-Rim [2, §2] and it is perhaps worthwhile mentioning that a special case of the present result was obtained by Buchsbaum-Eisenbud in a different context [1, Theorem 8.1].