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

T. Bandman   ; Yu. G. Zarhin

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 78 (2023) no. 1, pp. 1-64

Résumé

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.

Détail

Keywords: automorphism groups of compact complex manifolds, complex tori, conic bundles, Jordan properties of groups.
Mots-clés : algebraic dimension 0

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