Geometry and topology · Oct 6, 2026

The Global Spherical Shell conjecture

Every connected minimal compact complex surface of class VII with b2>0b_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 C2∖{0}\mathbb C^2\setminus\{0\} whose complement is connected.

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