  When a non-singular complex projective surface $X$ satisfies that $K_X\sim
0$, we shall show that there are only finitely many isomorphic classes as
abstract schemes in the set of moduli scheme of $H$-semistable sheaves with
fixed Chern classes $\alpha$ on $X$, where $H$ runs over the set of all
$\alpha$-generic polarizations on $X$.
