  We study constant Q-curvature metrics conformal to the round metric on the
sphere with finitely many point singularities. We show that the moduli space of
solutions with finitely many punctures in fixed positions, equipped with the
Gromov-Hausdorff topology, has the local structure of a real analytic variety
with formal dimension equal to the number of the punctures. If a nondegeneracy
hypothesis holds, we show that a neighborhood in the moduli space is actually a
real-analytic manifold of the expected dimension. We also construct a
geometrically natural set of parameters, construct a symplectic structure on
this parameter space and show that in the smooth case a small neighborhood of
the moduli space embeds as a Lagrangian submanifold in the parameter space.
