In his paper "Smooth models for elliptic threefolds" (In: The Birational Geometry of Degenerations, Progress in Mathematics, v. 29, Birkhauser, (1983), 85-133), Rick Miranda mentions in the example of section 8 (page 101-102) that it is an unfortunate fact of life that there are no small resolutions for the singularity of the threefold defined by the equation 


$$y^2=u^2+v^2+w^3\quad \text{in}\quad \mathbb{C}^4.$$


He said that it is a theorem of Brieskorn but he does not give a reference. Anyone has a reference to this theorem and its proof?


Updated (following some of the answers, the question can be generalized right away):


More generally the same question can be asked for 


$$y^2=u^2+v^2+w^{2k+1}\quad \text{in}\quad \mathbb{C}^4, \quad\text{where} \quad k \in \mathbb{N}\_0.$$



Non-existence of small resolutions for the singularity $y^2=u^2+v^2+w^3$
A $3$-dimensional hypersurface singularity of type $$y^2=u^2+v^2+w^k$$ admits a small resolution if and only if $k$ is even.
If $k$ is odd the corresponding singularity is factorial, so there is no small resolution. 


See the paper by R. Friedman [Simultaneous resolution of 3-fold double points](http://link.springer.com/article/10.1007%2FBF01458602), *Mathematische Annalen* **274** (1986), p. 675.


