Let X be a smooth complex projective variety. In 2002, Bridgeland [6] defined a notion of stability for the objects in 𝔇 b (X), the bounded derived category of coherent sheaves on X, which generalised the notion of slope stability for vector bundles on curves. There are many nice connections between stability conditions on X and the geometry of the variety. We construct new stability conditions for surfaces containing a curve C whose self-intersection is negative. We show that these stability conditions lie on a wall of the geometric chamber of Stab(X), the stability manifold of X.We then construct the moduli space Mσ (ℴ X ) of σ-semistable objects of class [ℴ X ] in K 0(X) after wall-crossing.

中文翻译：

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具有负自交曲线的曲面上的 Bridgeland 稳定性条件

让X是一个光滑的复射影变体。2002 年，Bridgeland [6] 为 𝔇 中的对象定义了稳定性概念 b (X)，相干滑轮的有界派生类别X，它概括了曲线上矢量束的斜率稳定性的概念。稳定性条件之间有很多很好的联系X以及品种的几何形状。我们为包含曲线的曲面构建了新的稳定性条件C其自交为负。我们表明，这些稳定性条件位于 Stab 几何室的壁上（X), 的稳定性流形X.然后我们构造模空间米σ (ℴ X ） 的σ- 类 [ℴ X ] 在ķ 0(X) 翻墙后。