Automorphism groups of $P^1$-bundles over a non-uniruled base

Abstract

In this survey we discuss holomorphic ${\mathbb{P}}^1$-bundles $p:X\to Y$ over a non-uniruled complex compact Kähler manifold $Y$, paying a special attention to the case when $Y$ is a complex torus. We discuss so called Jordan properties of the groups $Aut(X)$ and $Bim(X)$ of its biholomorphic and bimeromorphic automorphisms, respectively.

References in corpus (12)

• Jordan property for groups of birational selfmaps
• Jordan property for non-linear algebraic groups and projective varieties
• Finite group actions on homology spheres and manifolds with nonzero Euler characteristic
• Diffeomorphism Groups of Compact 4-manifolds are not always Jordan
• Finite group actions on manifolds without odd cohomology
• Automorphisms of pointless surfaces
• Jordan property for automorphism groups of compact spaces in Fujiki's class $C$
• Jordan property for algebraic groups and automorphism groups of projective varieties in arbitrary characteristic
• Bounded automorphism groups of compact complex surfaces
• Automorphisms of surfaces over fields of positive characteristic
• On the Kodaira problem for uniruled Kähler spaces
• Finite groups of bimeromorphic selfmaps of non-uniruled Kähler threefolds

Cited by in corpus (1)

• Finite group actions on abelian groups of finite Morley rank