Algebraic and complex geometry · Result 042

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

1 paper

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.

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Papers 1

Every complex K3 surface is Oka

OpenAI · 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 \(\mathbb C^m\to X\).

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Cite

@misc{OAI:Every-complex-K3-surface-is-Oka-September-23-2026,
  author = {{OpenAI}},
  title = {{Every complex K3 surface is Oka}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Every-complex-K3-surface-is-Oka-September-23-2026/paper.pdf}{OAI:Every-complex-K3-surface-is-Oka-September-23-2026}},
  year = {2026}
}

Formal verification

No Lean formalization is listed for this result yet. The repository notes that unformalized results could have issues.