  Using Ginzburg-Landau theory, we find novel configurations of vortices in
superconducting thin films subject to the magnetic field of a magnetic dot
array, with dipole moments oriented perpendicular to the film. Sufficiently
strong magnets cause the formation of vortex-antivortex pairs. In most cases,
the vortices are confined to dot regions, while the antivortices can form a
rich variety of lattice states. We propose an experiment in which the
perpendicular component of the dot dipole moments can be tuned using an
in-plane magnetic field. We show that in such an experiment the
vortex-antivortex pair density shows broad plateaus as a function of the dipole
strength. Many of the plateaus correspond to vortex configurations which break
dot lattice symmetries. In some of these states, the vortex cores are strongly
distorted. Possible experimental consequences are mentioned.
