Oka manifolds are ubiquitous

Abstract

We prove that a holomorphic family of connected complex Lie groups is Oka if and only if its base is Oka. We establish the Oka property for moduli spaces of stable and parabolic vector bundles and characterize Oka minimal \(\delta\)-regular abelian fibrations over compact curves by the nonnegativity of their orbifold Euler characteristic. Strong dominability, analytic extension, and holomorphic descent also yield applications to mapping spaces, character varieties, and compactified Jacobians.