Projectivity of analytic Hilbert quotients (Q2876093)

In the theory of group actions of complex reductive groups on complex spaces, Analytic Hilbert Quotients are the analogue of good quotients as considered in Geometric Invariant Theory. They arise naturally as momentum map quotients in the context of Hamiltonian group actions. We will relate the two quotient theories in the case of Hamiltonian group actions on complex algebraic varieties, proving projectivity of compact momentum map quotients in this case. Furthermore, we will present a projectivity result for complex spaces that admit a projective Analytic Hilbert Quotient.