The global spherical shell conjecture asserts that every connected minimal compact complex surface of class VII with positive second
Betti number contains a global
spherical shell. In the numerical formulation its hypotheses are
with no smooth rational curve of self-intersection .
The conclusion supplies a biholomorphic image of a neighborhood of in with connected complement.
.
The conclusion supplies a biholomorphic image of a neighborhood of 
in 
with connected complement.
