Are All Rational Manifolds Oka?

Determine whether every rational complex manifold has the Oka property.

Background

Corollary 3.5 shows that every compact rational manifold is algebraically Oka‑1 (aOka‑1), extending Runge-type approximation results to broad classes of targets. However, the stronger Oka property for rational manifolds is not established.

Resolving this would bridge a central gap in complex geometry, connecting rationality—a fundamental algebraic notion—to the strong holomorphic flexibility encoded by the Oka property.