A topological remark:

If $E \subset Y$ is a closed analytic subspace of a smooth space $X$, then the boundary
of a tubular neighbourhood is an (odd dimensional, real) sphere bundle over $E$.

Thus if the blowup of $Z \subset X$ is smooth then the boundary of a tubular 
neighbourhood of $Z \subset X$ can be written as a sphere bundle over the exceptional 
divisor $E = P(N_Z X)$.

One might use this to arrive at a contradiction e.g. by calculating cohomology.


Similar ideas were used by Mumford in his study of normal surface singularities.
[Mumford: The topology of normal singularities of an algebraic surface and a criterion for simplicity.][1]


  [1]: http://www.springerlink.com/content/b18270328x614668/