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arXiv · 2212.00393

The canonical trace of determinantal rings

Antonino Ficarra·Jürgen Herzog·Dumitru I. Stamate·Vijaylaxmi Trivedi
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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 $\mbox{tr}(\omega_R)$ 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 $\mbox{tr}(\omega_R)$ is generated by the $(n-2)$-minors of the Hilbert-Burch matrix of $I$.

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Antonino Ficarra, Jürgen Herzog, Dumitru I. Stamate, Vijaylaxmi Trivedi. 2022-12-01. The canonical trace of determinantal rings. https://arxiv.org/abs/2212.00393

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