We solve the BCS-Gor'kov equations for a pure, isotropic type-II super
conductor near the upper critical field. Corrections to the semiclassi
cal results lower the value of the upper critical field and cause H-c2
(T) to vanish quadratically near T-c. This form leads to positive curv
ature in the critical field, which has been seen in a range of materia
ls, and means that a type-II superconductor will convert to type I at
a temperature close to T-c.