For the derived category of bounded complexes of sheaves on a smoothprojective surface, Bridgeland and Arcara-Bertram constructed Bridgelandstability 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 aresult of Bayer by proving that the moduli of polynomial Bridgeland semistableobjects of a fixed numerical type coincides with the moduli of $(Z_m, \mathcalP_m)$-semistable objects whenever $m$ is larger than a universal constantdepending only on the numerical type. We further identify the moduli ofpolynomial Bridgeland semistable objects with the Gieseker/Simpson modulispaces and the Uhlenbeck compactification spaces.
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机译：对于光滑投影面上的滑轮的有界复合物的派生类别，Bridgeland和Arcara-Bertram构造了Bridgelandstability条件$（Z_m，\ mathcal P_m）$，参数为$ m \ in（0，+ \ infty）$。在本文中，我们证明了固定数值类型$（0，+ \ infty）$中的微型墙的集合是局部有限的。此外，我们证明了固定数值类型的多项式Bridgeland半稳定对象的模与$（Z_m，\ mathcalP_m）$-半对称对象的模数一致，只要$ m $大于仅依赖于常数的通用常数，我们就加强了Bayer的研究成果。数值类型。我们进一步用Gieseker / Simpson模空间和Uhlenbeck压缩空间确定多项式Bridgeland半稳定对象的模。
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