Oka classification for minimal compact complex surfaces: Kodaira dimension zero and class VII

Proves that every complex K3 surface is Oka, including nonprojective surfaces. More generally, every connected minimal compact complex surface of Kodaira dimension zero is Oka; a connected minimal compact complex surface of class VII is Oka exactly when it is a Hopf or Enoki surface.

Manuscript

Every complex K3 surface is Oka

September 23, 2026 · source · cite as \cite{OAI:Every-complex-K3-surface-is-Oka-September-23-2026}

We prove that every complex K3 surface X is Oka, resolving the K3 Oka conjecture. Equivalently, for every m ≥ 1, every holomorphic map to X from a neighborhood of a compact convex set in ℂ^m can be approximated uniformly on that set by entire maps \mathbb C^m\to X.

Result 042 · Algebraic and complex geometry. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.