  We study the behavior of the Gieseker space of semistable torsion-free
sheaves of rank r and fixed c_1, c_2 on a non-singular projective surface as
the polarization varies. It is shown that the ample cone admits a locally
finite chamber structure, and that passing a wall adjacent to a pair of
chambers has the effect of modifying the moduli space by a (finite) sequence of
flips of the type studied by Thaddeus. The key steps are a modification of
Simpson's method and the introduction of a "rationally twisted" moduli space.
The result is more general but less explicit than the recent work of
Ellingsrud-Goettsche (alg-geom/9410005) and Friedman-Qin (alg-geom/9410007).
