On $G/N$-Hilb of $N$-Hilb

In this paper we consider the iterated G-equivariant Hilbert scheme G/N-Hilb(N-Hilb) and prove that G/N-Hilb(N-Hilb(C-3)) is a crepant resolution of C-3/G isomorphic to the moduli space M-theta(Q) of theta-stable representations of the McKay quiver Q for certain stability condition theta. We provide several explicit examples to illustrate this construction. We also consider the problem of when G/N-Hilb(N-Hilb) is isomorphic to G-Hilb showing the fact that these spaces are most of the times different.