CATALOGUE 042
Oka classification for K3 surfaces and other compact complex surfaces
The official catalogue contains one manuscript. Its central claim is the Oka property for every complex K3 surface, with consequences for dense entire immersions, Oka classification in Kodaira dimension zero and minimal class VII, and global sprays on projective K3 and Enriques surfaces.
The one manuscript in official catalogue order
These summaries give the principal scope; consult the cited original results for the complete hypotheses and statements.
Page counts include references. On narrow screens, scroll the table sideways.
| # | Manuscript and overview | Principal claim | Role and available overview |
|---|---|---|---|
| 01 | Every complex K3 surface is Oka →Short name: K3 OkaSeptember 23, 2026 · 56 pagesOriginal paper (GitHub) ↗ | CAP for every complex K3. Minimal κ=0 surfaces are Oka; in minimal class VII, exactly Hopf and Enoki are Oka. Projective K3 and Enriques surfaces are elliptic. Theorem 1.1 · p. 2; Corollaries 10.2–10.3 · p. 54 ↗ | Two strip directions give local extension and convex approximation; Torelli transfers three period cases. Separate inputs supply interpolation, classification, and sprays. Read the proof overview → |
Connections to external results
The proof overview treats the three rationality types of periods, supplies a local operation at every point, and passes to convex approximation in every source dimension. Each stated conclusion is linked to its explanation.
Official catalogue 060, Global Spherical Shells on Minimal Surfaces of Class VII, is used in the minimal class-VII classification to reduce the positive-second-Betti-number case to Kato surfaces. It is not used in the K3 main theorem. The input list records the other external results and application conditions.
Sources and checking scope
The official subject is Algebraic and complex geometry. The official overview dated October 6, 2026 uses the title above; CONTENTS instead says Oka classification for minimal compact complex surfaces: Kodaira dimension zero and class VII.
OpenAI Research Catalog · Catalogue 042 · p. 6
The manuscript is the September 23, 2026 version, 56 pages. The reading covers the main statements, selected proof passages, all consequence cases, and specified external input statements. It is not an independent verification of every proof. Outstanding analytic estimates, geometric constructions, and further external inputs are listed in the article's final section.
This guide and article are AI-generated reading aids. Important mathematical claims and proofs should be checked against the originals.