The Monodromy Map from Differential Systems to the Character Variety Is Generically Immersive

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-11-09 DOI:10.4171/prims/59-4-5

Indranil Biswas, Sorin Dumitrescu

引用次数: 0

Abstract

Let $G$ be a connected reductive affine algebraic group defined over $\mathbb C$ and $\mathfrak g$ its Lie algebra. We study the monodromy map from the space of $\mathfrak g$-differential systems on a compact connected Riemann surface $\Sigma$ of genus $g \,\geq\, 2$ to the character variety of $G$-representations of the fundamental group of $\Sigma$. If the complex dimension of $G$ is at least three, we show that the monodromy map is an immersion at the generic point.

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从微分系统到角色多样性的单一性映射通常是沉浸式的

设$G$是在$\mathbb C$和$\mathfrak g$的李代数上定义的连通约化仿射代数群。我们研究了紧连通黎曼曲面$\Sigma$属$g \,\geq\, 2$上的$\mathfrak g$ -微分系统空间到$\Sigma$基本群的$G$ -表示的特征变化的单映射。如果$G$的复维数至少为3，则表明单形图在一般点是浸入式的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.