  Moduli spaces of semistable sheaves on a K3 or abelian surface with respect
to a general ample divisor are shown to be locally factorial, with the
exception of symmetric products of a K3 or abelian surface and the class of
moduli spaces found by O'Grady. Consequently, since singular moduli space that
do not belong to these exceptional cases have singularities in codimension
$\geq4$ they do no admit projective symplectic resolutions.
