Oka classification for K3 surfaces and other compact complex surfaces at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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Oka classification for K3 surfaces and other compact complex surfaces

at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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Difficulty:	🧠🧠🧠🧠🧠	Ages:	13 - ∞
Skills:	shapes made of equations	Levels:	1
Category:	Algebraic and complex geometry	Lean version:	not yet
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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.

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LEVEL 1 Every complex K3 surface is Oka

released 2026-09-23 | 4 theorems · 26 lemmas · 39 proofs · 27,647 words | PLAY LEVEL 1 » (pdf)

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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