  We consider the fundamental solution to the wave equation on a manifold with
corners of arbitrary codimension. If the initial pole of the solution is
appropriately situated, we show that the singularities which are diffracted by
the corners (i.e., loosely speaking, are not propagated along limits of
transversely reflected rays) are smoother than the main singularities of the
solution. More generally, we show that subject to a hypothesis of nonfocusing,
diffracted wavefronts of any solution to the wave equation are smoother than
the incident singularities. These results extend our previous work on edge
manifolds to a situation where the fibers of the boundary fibration, obtained
here by blowup of the corner in question, are themselves manifolds with
corners.
