  We show that a complex manifold M in the boundary of a smooth bounded
pseudoconvex domain in C^n is an obstruction to compactness of the
d-bar-Neumann operator on the domain, provided that at some point of M, the
Levi form has the maximal possible rank n-1-dim(M) (i.e. the domain is strictly
pseudoconvex in the directions transverse to M). In particular, an analytic
disc is an obstruction, provided that at some point of the disc, the Levi form
has only one zero eigenvalue. We also show that a boundary point where the Levi
form has only one zero eigenvalue can be picked up by the plurisubharmonic hull
of a set only via an analytic disc in the boundary.
