The canonical bundle of a
realizable CR hypersurface has closed sections. Examples are given of non-realizable
hypersurfaces with closed sections and others without such sections. If however an
abstract CR hypersurface of dimension 2m + 1 has m strongly independent CR
functions then a closed section can be used to produce the missing function and so
assures that the hypersurface is realizable. The existence of a closed section is
equivalent to a condition on the range of ∂b acting on functions. Some non-realizable
CR hypersurfaces are shown to have ∂b-cohomology groups quite different from those
of realizable hypersurfaces.
