  This paper shows that the mass-sheet degeneracy and other degeneracies in
lensing have simple geometrical interpretations: they are mostly rescalings of
the arrival-time surface. Different degeneracies appear in Local Group lensing
and in cosmological lensing, because in the former the absolute magnification
is measured but the image structure is not resolved, whereas in the latter the
reverse usually applies. The most dangerous of these is a combination we may
call the `mass-disk degeneracy' in multiply-imaging galaxy lenses, which may
lead to large systematic uncertainties in estimates of cosmological parameters
from these systems.

Astrophysics