  We test a recently proposed wall-crossing formula for the change of the
Hilbert space of BPS states in d=4,N=2 theories. We study decays of D4D2D0
systems into pairs of D4D2D0 systems and we show how the wall-crossing formula
reproduces results of Goettsche and Yoshioka on wall-crossing behavior of the
moduli of slope-stable holomorphic bundles over holomorphic surfaces. Our
comparison shows very clearly that the moduli space of the D4D2D0 system on a
rigid surface in a Calabi-Yau is not the same as the moduli space of torsion
free sheaves, even when worldhseet instantons are neglected. Moreover, we argue
that the physical formula should make some new mathematical predictions for a
future theory of the moduli of stable objects in the derived category.
