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

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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。

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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.

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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.