  Within the phenomenological Ginzburg-Landau theory, we demonstrate the
enhancement of superconductivity in a superconducting film, when nanostructured
by a lattice of magnetic particles. Arrays of out-of-plane magnetized dots
(MDs) extend the critical magnetic field and critical current the sample can
sustain, due to the interaction of the vortex-antivortex pairs and surrounding
supercurrents induced by the dots and the external flux lines. Depending on the
stability of the vortex-antivortex lattice, a peak in the Hext-T boundary is
found for applied integer and rational matching fields, which agrees with
recent experiments [Lange et al., Phys. Rev. Lett. 90, 197006 (2003)]. Due to
compensation of MDs- and Hext-induced currents, we predict the field-shifted
jc-Hext characteristics, as was actually realized in previous experiment but
not commented on [Morgan and Ketterson, Phys. Rev. Lett. 80, 3614 (1998)].
