Antonino Ficarra, Jürgen Herzog, Dumitru I. Stamate, Vijaylaxmi Trivedi
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引用次数: 0
摘要
我们计算了一般行列式环的典型迹，并提供了迹特殊化的充分条件。作为应用，我们确定了一般为戈伦斯坦的二维科恩-麦考莱环 R 的典型迹 \(tr (\omega _R)\)。研究表明，如果 R 的定义理想 I 由 n 个元素生成，那么 \(tr (\omega _R)\) 是由 I 的希尔伯特-伯奇矩阵的 \((n-2)\)-最小值生成的。
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.
期刊介绍：
Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.
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