  Suppose a compact Lie group acts on a polarized complex projective manifold
(M,L). Under favorable circumstances, the Hilbert-Mumford quotient for the
action of the complexified group may be described as a symplectic quotient (or
reduction). This paper addresses some metric questions arising from this
identification, by analyzing the relationship between the Szego kernel of the
pair (M,L) and that of the quotient.
