  This paper studies aspects of ``holography'' for Euclidean signature pure
gravity on asymptotically AdS 3-manifolds. This theory can be described as
SL(2,C) CS theory. However, not all configurations of CS theory correspond to
asymptotically AdS 3-manifolds. We show that configurations that do have the
metric interpretation are parameterized by the so-called projective structures
on the boundary. The corresponding asymptotic phase space is shown to be the
cotangent bundle over the Schottky space of the boundary. This singles out a
``gravitational'' sector of the SL(2,C) CS theory. It is over this sector that
the path integral has to be taken to obtain the gravity partition function. We
sketch an argument for holomorphic factorization of this partition function.
