We revisit generalized K$\ddot{ a}$hler reduction introduced by Lin and Tolman in \cite{ LT} from a viewpoint of geometric invariant theory. It is shown that in the strong Hamiltonian case introduced in the present paper, many well-known conclusions of ordinary K$\ddot{ a}$hler reduction can be generalized without much effort to the generalized setting. It is also shown how generalized holomorphic structures arise naturally from the reduction procedure.
Categories: math.DG math.CV math.SG