  Using combinatorial properties of complex reflection groups, we show that the
generalised Calogero-Moser space associated to the centre of the corresponding
rational Cherednik algebra is singular for all values of its deformation
parameter c if and only if the group is different from the wreath product
$S_n\wr C_m$ and the binary tetrahedral group. This result and a theorem of
Ginzburg and Kaledin imply that there does not exist a symplectic resolution of
the singular symplectic variety h+h*/W outside of these cases; conversely we
show that there exists a symplectic resolution for the binary tetrahedral group
(Hilbert schemes provide resolutions for the wreath product case).
