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 $tr({\omega }_R)$ 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 $tr({\omega }_R)$ is generated by the $(n-2)$-minors of the Hilbert-Burch matrix of $I$.