D-branes on Orbifolds and Topology Change

We consider D-branes on an orbifold $C^3/Z_n$ and investigate the moduli space of the D-brane world-volume gauge theory by using toric geometry and gauged linear sigma models. For $n=11$, we find that there are five phases, which are topologically distinct and connected by flops to each other. We also verify that non-geometric phases are projected out for $n=7,9,11$ cases as expected. Resolutions of non-isolated singularities are also investigated.