  We formulate the effective field theory of a D-particle on orbifolds of $T^4$
by a cyclic group as a gauge theory in a $V$-bundle over the dual orbifold. We
argue that this theory admits Fayet-Iliopoulos terms analogous to those present
in the case of noncompact orbifolds. In the $n=2$ case, we present some
evidence that turning on such terms resolves the orbifold singularities and may
lead to a $K3$ surface realized as a blow up of the fixed points of the cyclic
group action.
