  A theorem of Mumford states that, on complex surfaces, any normal isolated
singularity whose link is diffeomorphic to a sphere is actually a smooth point.
While this property fails in higher dimensions, McLean asks whether the contact
structure that the link inherits from its embedding in the variety may suffice
to characterize smooth points among normal isolated singularities. He proves
that this is the case in dimension 3. In this paper, we use techniques from
birational geometry to extend McLean's result to a large class of higher
dimensional singularities. We also introduce a more refined invariant of the
link using CR geometry, and conjecture that this invariant is strong enough to
characterize smoothness in full generality.
