The canonical trace of determinantal rings
Abstract
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(ωR) 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(ωR) is generated by the (n-2)-minors of the Hilbert-Burch matrix of I.
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