  We investigate the occurrence of various exotic spacelike singularities in
the past and the future evolution of $k = \pm 1$ Friedmann-Robertson-Walker
model and loop quantum cosmology using a sufficiently general phenomenological
model for the equation of state. We highlight the non-trivial role played by
the intrinsic curvature for these singularities and the new physics which
emerges at the Planck scale. We show that quantum gravity effects generically
resolve all strong curvature singularities including big rip and big freeze
singularities. The weak singularities, which include sudden and big brake
singularities are ignored by quantum gravity when spatial curvature is
negative, as was previously found for the spatially flat model. Interestingly,
for the spatially closed model there exist cases where weak singularities may
be resolved when they occur in the past evolution. The spatially closed model
exhibits another novel feature. For a particular class of equation of state,
this model also exhibits an additional physical branch in loop quantum
cosmology, a baby universe separated from the parent branch. Our analysis
generalizes previous results obtained on the resolution of strong curvature
singularities in flat models to isotropic spacetimes with non-zero spatial
curvature.
