On the complex structure of symplectic quotients.

Let K be a compact group. For a symplectic quotient M_λ of a compact Hamiltonian Kähler K-manifold, we show that the induced complex structure on M_λ is 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. [ABSTRACT FROM AUTHOR]