  We study the modulational instability induced by periodic variations of
group-velocity dispersion in the proximity of the zero dispersion point.
Multiple instability peaks originating from parametric resonance coexist with
the conventional modulation instability due to fourth order dispersion, which
in turn is suppressed by the oscillations of dispersion. Moreover isolated
unstable regions appear in the space of parameters due to imperfect phase
matching. This confirms the dramatic effect of periodic tapering in the control
and shaping of MI sidebands in optical fibers.
