CATALOGUE 060
The Global Spherical Shell conjecture
This catalogue concerns the claim that every minimal class VII surface with positive second Betti number contains a global spherical shell. Its single manuscript constructs rational curves through weighted analysis on a cyclic cover and reduces the conclusion to established curve criteria.
1. Paper in this catalogue
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 | Global Spherical Shells on Minimal Surfaces of Class VII →Short name: Global Spherical ShellsSeptember 24, 2026 · 39 pagesOriginal paper (GitHub) ↗ | Claims that a connected minimal compact class VII surface with $b_2>0$ admits a holomorphically embedded neighborhood of the standard $S^3$ with connected complement. Theorem 1.1 · p. 1 ↗ | After the square-zero-divisor case, passes from relative Chern classes on the cyclic cover through sections and compact components to a rational-curve count and a shell criterion. Read the proof overview → |
2. Connection to another catalogue
Theorem 1.1 of Global Spherical Shells on Minimal Surfaces of Class VII is used in the class VII step of Every complex K3 surface is Oka. Corollary 10.2 of the latter manuscript uses it to place minimal class VII surfaces with $b_2>0$ in the Kato classification and then applies established Oka criteria. The input is confined to the class VII part of that corollary; it does not enter the K3 theorem or the Enriques and Kodaira-dimension-zero parts.
3. Sources and checking scope
The official heading for 060 is The Global Spherical Shell conjecture, in Algebraic and complex geometry. The consulted overview places that subject in the catalogue-number range 032–069 and lists 060 on PDF p.8. Actual entries follow the official list without filling gaps in the numbering.
OpenAI Research Catalog · 060 · p. 8
The manuscript is the September 24, 2026 version, with 39 pages. Comparisons cover the hypotheses and every conclusion of Theorem 1.1, its route through §§2–7, the main external shell-criterion statements, and the use in Corollary 10.2 of catalogue 042. Independent verification of all analytic estimates and original-source comparison of some external inputs remain open, as specified in the article’s checking scope. Describing the manuscript’s claim is distinct from certifying the complete proof.