Every connected minimal compact complex surface of class VII with b_2\gt 0 contains a global spherical shell, proving the positive-b2 Global Spherical Shell conjecture. Such a shell is a holomorphically embedded neighborhood of the standard three-sphere in \mathbb C^2\setminus\{0\} whose complement is connected.
Manuscript
Global Spherical Shells on Minimal Surfaces of Class VII
September 24, 2026 · source · cite as \cite{OAI:Global-Spherical-Shells-on-Minimal-Surfaces-of-Class-VII-September-24-2026}
We prove the Global Spherical Shell conjecture: every connected minimal compact complex surface of class VII with positive second Betti number contains a global spherical shell. This is a holomorphically embedded neighborhood of the standard three-sphere in \mathbb C^2\setminus\{0\} whose complement is connected.
Result 060 · 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.
Source: https://github.com/openai/math/blob/main/CONTENTS.md