On the complex structure of symplectic quotients

Let K be a compact group. For a symplectic quotient Mof a compact Hamiltonian K?hler Kmanifold, we show that the induced complex structure on Mis locally invariant when the parameter λ varies in Lie(K)~*. To prove such a result, we take two different approaches:(i) use the complex geometry properties of the symplectic implosion construction;(ii) investigate the variation of geometric invariant theory(GIT) quotients.