The Global Spherical Shell conjecture at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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The Global Spherical Shell conjecture

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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The Global Spherical Shell conjecture. 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.

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LEVEL 1 Global Spherical Shells on Minimal Surfaces of Class VII

released 2026-09-24 | 3 theorems · 17 lemmas · 32 proofs · 19,730 words | PLAY LEVEL 1 » (pdf)

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.

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