  The prescribed Ricci curvature problem in the context of G-invariant metrics
on a homogeneous space M=G/K is studied. We focus on the metrics at which the
Ricci curvature map is, locally, as injective and surjective as it can be. Our
main result is that such property is generic in the compact case. Our main tool
is a formula for the Lichnerowicz Laplacian we prove in terms of the moment map
for the variety of algebras.
