On the complex structure of symplectic quotients

Let $K$ be a compact group. For symplectic quotient $M_{\lambda}$ of Hamiltonian K\"ahler $K$-manifold, we show that the induced complex structure on is locally invariant when parameter $\lambda$ varies in $\mathrm{Lie}(K)^*$. To prove such result, take two different approaches: (i) by using geometry properties implosion construction; (ii) investigating variation GIT quotients.