行列式环的典型痕量

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2024-09-14 DOI:10.1007/s00013-024-02047-0

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

{"title":"行列式环的典型痕量","authors":"Antonino Ficarra, Jürgen Herzog, Dumitru I. Stamate, Vijaylaxmi Trivedi","doi":"10.1007/s00013-024-02047-0","DOIUrl":null,"url":null,"abstract":"<div>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.</div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The canonical trace of determinantal rings\",\"authors\":\"Antonino Ficarra, Jürgen Herzog, Dumitru I. Stamate, Vijaylaxmi Trivedi\",\"doi\":\"10.1007/s00013-024-02047-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>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.</div>\",\"PeriodicalId\":8346,\"journal\":{\"name\":\"Archiv der Mathematik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-09-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Archiv der Mathematik\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00013-024-02047-0\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archiv der Mathematik","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00013-024-02047-0","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

The canonical trace of determinantal rings

查看原文本刊更多论文

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

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.