The canonical trace of determinantal rings

We compute the canonical trace of generic determinantal rings and provide a sufficient condition for the trace to specialize. As an application, we determine the canonical trace \(tr (\omega _R)\) $tr({\omega }_R)$ of a Cohen–Macaulay ring R of codimension two, which is generically Gorenstein. It is shown that if the defining ideal I of R is generated by n elements, then \(tr (\omega _R)\) $tr({\omega }_R)$ is generated by the \((n-2)\) $(n-2)$ -minors of the Hilbert–Burch matrix of I.