有限群方案在曲线上的作用

IF 0.5 4区数学 Q3 MATHEMATICS

Pure and Applied Mathematics Quarterly Pub Date : 2024-05-15 DOI:10.4310/pamq.2024.v20.n3.a2

Michel Brion

{"title":"有限群方案在曲线上的作用","authors":"Michel Brion","doi":"10.4310/pamq.2024.v20.n3.a2","DOIUrl":null,"url":null,"abstract":"Every action of a finite group scheme $G$ on a variety admits a projective equivariant model, but not necessarily a normal one. As a remedy, we introduce and explore the notion of $G$-normalization. In particular, every curve equipped with a $G$-action has a unique projective $G$-normal model, characterized by the invertibility of ideal sheaves of all orbits. Also, $G$-normal curves occur naturally in some questions on surfaces in positive characteristics.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Actions of finite group schemes on curves\",\"authors\":\"Michel Brion\",\"doi\":\"10.4310/pamq.2024.v20.n3.a2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Every action of a finite group scheme $G$ on a variety admits a projective equivariant model, but not necessarily a normal one. As a remedy, we introduce and explore the notion of $G$-normalization. In particular, every curve equipped with a $G$-action has a unique projective $G$-normal model, characterized by the invertibility of ideal sheaves of all orbits. Also, $G$-normal curves occur naturally in some questions on surfaces in positive characteristics.\",\"PeriodicalId\":54526,\"journal\":{\"name\":\"Pure and Applied Mathematics Quarterly\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-05-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Pure and Applied Mathematics Quarterly\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/pamq.2024.v20.n3.a2\",\"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":"Pure and Applied Mathematics Quarterly","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/pamq.2024.v20.n3.a2","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

有限群方案 $G$ 在一个综上的每个作用都有一个投影等变模型，但不一定是正态模型。作为一种补救措施，我们引入并探讨了$G$正则化的概念。特别是，每一条配备了 $G$ 作用的曲线都有一个唯一的投影 $G$ 正态模型，其特征是所有轨道的理想剪切的不可逆性。此外，$G$正态曲线自然出现在一些关于正特征曲面的问题中。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Actions of finite group schemes on curves

Every action of a finite group scheme $G$ on a variety admits a projective equivariant model, but not necessarily a normal one. As a remedy, we introduce and explore the notion of $G$-normalization. In particular, every curve equipped with a $G$-action has a unique projective $G$-normal model, characterized by the invertibility of ideal sheaves of all orbits. Also, $G$-normal curves occur naturally in some questions on surfaces in positive characteristics.

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

Pure and Applied Mathematics Quarterly 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high-quality, original papers on all fields of mathematics. To facilitate fruitful interchanges between mathematicians from different regions and specialties, and to effectively disseminate new breakthroughs in mathematics, the journal welcomes well-written submissions from all significant areas of mathematics. The editors are committed to promoting the highest quality of mathematical scholarship.