  Magnetically charged Abelian defects are shown to arise on most compact base
manifolds and in most Abelian projection gauges. They obey the Dirac
quantisation condition and give rise to homogeneous magnetic background fields.
The reasons for their occurrence are global failures of the procedure with
which gauge covariant operators are diagonalised or their eigenphases
extracted. Defects related to the former case are string-like; for the latter
case they resemble domain walls. Either configuration forms the generic case
and indicates a failure of gauge fixing as continuity and periodicity
properties of the functional space are changed. These results are first
obtained in canonically quantised QCD_{3+1} and path integral QCD_{2+1} on the
torus for the modified axial gauge which keeps only the eigenphases as
dynamical variables of the Wilson line in the x_3-direction. In the end, they
are extended to other gauges, dimensions and standard manifolds.
