Blow-up at a Single Point: Does Oka Persist?

Determine whether the blow-up of any Oka manifold at a single point remains an Oka manifold.

Background

The authors discuss bimeromorphic invariance issues in Oka theory. Kusakabe showed that blow-ups at certain non-tame discrete sets yield manifolds that are Brody volume-hyperbolic and thus not Oka, while blow-ups along tame centers can be Oka via weak subellipticity.

Despite these advances, the specific case of blowing up an Oka manifold at a single point remains unresolved, representing a fundamental question about the stability of the Oka property under simple birational modifications.