  For the derived category of bounded complexes of sheaves on a smooth
projective surface, Bridgeland and Arcara-Bertram constructed Bridgeland
stability conditions $(Z_m, \mathcal P_m)$ parametrized by $m \in (0,
+\infty)$. In this paper, we show that the set of mini-walls in $(0, +\infty)$
of a fixed numerical type is locally finite. In addition, we strengthen a
result of Bayer by proving that the moduli of polynomial Bridgeland semistable
objects of a fixed numerical type coincides with the moduli of $(Z_m, \mathcal
P_m)$-semistable objects whenever $m$ is larger than a universal constant
depending only on the numerical type. We further identify the moduli of
polynomial Bridgeland semistable objects with the Gieseker/Simpson moduli
spaces and the Uhlenbeck compactification spaces.

Algebraic Geometry