零维完全交点Tjurina数的一个尖锐下界

Pub Date : 2023-09-05 DOI:10.1134/S001626632301001X
A. G. Aleksandrov
{"title":"零维完全交点Tjurina数的一个尖锐下界","authors":"A. G. Aleksandrov","doi":"10.1134/S001626632301001X","DOIUrl":null,"url":null,"abstract":"<p> As is known, for isolated hypersurface singularities and complete intersections of positive dimension, the Milnor number is the least upper bound for the Tjurina number, i.e., <span>\\(\\tau \\leqslant \\mu\\)</span>. In this paper we show that, for zero-dimensional complete intersections, the reverse inequality holds. The proof is based on properties of faithful modules over an Artinian local ring. We also exploit simple properties of the annihilator and the socle of the modules of Kähler differentials and derivations and the theory of duality in the cotangent complex of zero-dimensional singularities. </p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On a Sharp Lower Bound for the Tjurina Number of Zero-Dimensional Complete Intersections\",\"authors\":\"A. G. Aleksandrov\",\"doi\":\"10.1134/S001626632301001X\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> As is known, for isolated hypersurface singularities and complete intersections of positive dimension, the Milnor number is the least upper bound for the Tjurina number, i.e., <span>\\\\(\\\\tau \\\\leqslant \\\\mu\\\\)</span>. In this paper we show that, for zero-dimensional complete intersections, the reverse inequality holds. The proof is based on properties of faithful modules over an Artinian local ring. We also exploit simple properties of the annihilator and the socle of the modules of Kähler differentials and derivations and the theory of duality in the cotangent complex of zero-dimensional singularities. </p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-09-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S001626632301001X\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S001626632301001X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

众所周知,对于孤立的超曲面奇点和正维的完全交点,Milnor数是Tjurina数的最小上界,即\(\tau \leqslant \mu\)。本文证明,对于零维完全交,逆不等式成立。该证明是基于阿提尼局部环上的忠实模的性质。我们还利用了零维奇点的余切复合体中的湮灭子和Kähler的微分和导数的模的简单性质以及对偶理论。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
分享
查看原文
On a Sharp Lower Bound for the Tjurina Number of Zero-Dimensional Complete Intersections

As is known, for isolated hypersurface singularities and complete intersections of positive dimension, the Milnor number is the least upper bound for the Tjurina number, i.e., \(\tau \leqslant \mu\). In this paper we show that, for zero-dimensional complete intersections, the reverse inequality holds. The proof is based on properties of faithful modules over an Artinian local ring. We also exploit simple properties of the annihilator and the socle of the modules of Kähler differentials and derivations and the theory of duality in the cotangent complex of zero-dimensional singularities.

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
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信