Change of Polarization for Moduli of Sheaves on Surfaces as Bridgeland Wall-crossing

We prove that the "Thaddeus flips" of L-twisted sheaves constructed by Matsuki and Wentworth explaining the change of polarization for Gieseker semistable sheaves on a surface can be obtained via Bridgeland wall-crossing. Similarly, we realize the change of polarization for moduli spaces of one-dimensional Gieseker semistable sheaves on a surface by varying a family of stability conditions.