Flops and equivalences of derived categories for threefolds with only terminal Gorenstein singularities

We prove that Bridgeland's moduli space of perverse point sheaves for certain flopping contractions gives the flops, and the Fourier-Mukai transform given by the birational correspondence of the flop is an equivalence between bounded derived categories. The main techniques used in the proof are: (1) Techniques developed in [BKR99] to prove equivalences of derived categories using moduli spaces and Fourier-Mukai transformations. (2) Bridgeland's results [Br00] on smooth threefold flops. (3) Deformation theory of local terminal Gorenstein flops.