Automorphism groups of $P^1$-bundles over a non-uniruled base
- Resource Type
- Working Paper
- Authors
- Bandman, Tatiana; Zarhin, Yuri G.
- Source
- Uspekhi Mat. Nauk, 78:1(469) (2023), 3--66
- Subject
- Mathematics - Complex Variables
Mathematics - Algebraic Geometry
32M05, 32M18, 32L05, 32J18, 32J27, 14J50, 57S25
- Language
In this survey we discuss holomorphic $\mathbb{P}^1$-bundles $p: X \to Y$ over a non-uniruled complex compact K\"ahler manifold $Y$, paying a special attention to the case when $Y$ is a complex torus. We discuss so called Jordan properties of the groups $Aut(X)$ and $Bim(X)$ of its biholomorphic and bimeromorphic automorphisms, respectively.