  We give an existence result on (H,A)-stable sheaves on a K3 or abelian
surface X with primitive triple of invariants (rank,first Chern class,Euler
characteristics) in the integral cohomology lattice. Such a result yields the
existence of singular projective Q-factorial symplectic terminalisations of
certain moduli spaces of sheaves on X that are Gieseker semistable with respect
to a nongeneral ample divisor.
