# Mini-walls for Bridgeland stability conditions on the derived category of sheaves over surfaces

@article{Lo2011MiniwallsFB,
title={Mini-walls for Bridgeland stability conditions on the derived category of sheaves over surfaces},
author={Jason Lo and Zhenbo Qin},
journal={Asian Journal of Mathematics},
year={2011},
volume={18},
pages={321-344}
}
• Published 22 March 2011
• Mathematics
• Asian Journal of Mathematics
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…

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