非规则基上$\mathbb{P}^1$-束的自同构群

IF 1.4 4区数学 Q1 MATHEMATICS

Russian Mathematical Surveys Pub Date : 2023-01-01 DOI:10.4213/rm10093e

Tatiana Bandman, Yuri Gennad'evich Zarhin

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引用次数: 0

摘要

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。

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

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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来源期刊

Russian Mathematical Surveys 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Mathematical Surveys is a high-prestige journal covering a wide area of mathematics. The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The survey articles on current trends in mathematics are generally written by leading experts in the field at the request of the Editorial Board.