The canonical trace of determinantal rings

Antonino Ficarra; Jürgen Herzog; Dumitru I. Stamate; Vijaylaxmi Trivedi

The canonical trace of determinantal rings

Commutative Algebra 2022-12-06 v2

Authors: Antonino Ficarra , Jürgen Herzog , Dumitru I. Stamate , Vijaylaxmi Trivedi

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 $I$ .

Keywords

determinantal rings canonical trace cohen-macaulay ring hilbert-burch matrix gorenstein codimension two

Cite

@article{arxiv.2212.00393,
  title  = {The canonical trace of determinantal rings},
  author = {Antonino Ficarra and Jürgen Herzog and Dumitru I. Stamate and Vijaylaxmi Trivedi},
  journal= {arXiv preprint arXiv:2212.00393},
  year   = {2022}
}

The canonical trace of determinantal rings

Abstract

Keywords

Cite

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