Automorphism groups of $\mathbb{P}^1$-bundles over a non-uniruled base

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.4213/rm10093e

Tatiana Bandman, Yuri Gennad'evich Zarhin

引用次数: 0

Abstract

In this survey we discuss holomorphic $\mathbb{P}^1$-bundles $p\colon X \to Y$ over a non-uniruled complex compact Kähler manifold $Y$, paying a special attention to the case when $Y$ is a complex torus. We consider the groups $\operatorname{Aut}(X)$ and $\operatorname{Bim}(X)$ of its biholomorphic and bimeromorphic automorphisms, respectively, and discuss when these groups are bounded, Jordan, strongly Jordan, or very Jordan. Bibliography: 88 titles.

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非规则基上$\mathbb{P}^1$-束的自同构群

本文讨论了非规则复紧Kähler流形$Y$上的全纯$\mathbb{P}^1$-束$ P \冒号X \到Y$，特别注意了$Y$是复环面的情况。分别考虑其生物全纯自同构和双亚纯自同构的群$\operatorname{Aut}(X)$和$\operatorname{Bim}(X)$，并讨论了这些群何时是有界的、约旦、强约旦和非常约旦。参考书目:88种。

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.