D-particles on T-4/Z(n) orbifolds and their resolutions

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 non-compact orbifolds. In the n = 2 case, we present some evidence that turning on such terms resolves the orbifold singulariti es and may lead to a K3 surface realized as a blow up of the fixed points o f the cyclic group action. (C) 1999 Published by Elsevier Science B.V.