标题： 一个有趣的墙交叉：墙交叉/MMP对应关系的失败 显示英文标题

标题： An interesting wall-crossing: Failure of the wall-crossing/MMP correspondence

摘要： 我们证明了Bridgeland稳定性中的墙交叉无法被稳定层的双有理几何所检测到，反之亦然。 在典范亏格四曲线的稳定性空间中存在一条墙，这条墙不会在极小模型程序中引起一个步骤。 更准确地说，我们给出了$\mathrm{D}^{b}(\mathbb{P}^{3})$中的一组墙交叉的例子，其中：该墙会诱导与相邻房间之一相关的稳定对象模空间的小收缩，但会对另一个房间引起除子收缩。 这显著地复杂化了这一对应关系的整体图景，从而影响了稳定性条件在代数几何中的应用。 显示英文摘要

摘要： We show that the wall-crossing in Bridgeland stability fails to be detected by the birational geometry of stable sheaves, and vice versa. There is a wall in the stability space of canonical genus four curves which does not induce a step in the Minimal Model Program. More precisely, we give an example of a wall-crossing in $\mathrm{D}^{b}(\mathbb{P}^{3})$ such that: the wall induces a small contraction of the moduli space of stable objects associated to one of the adjacent chambers, but a divisorial contraction to the other. This significantly complicates the overall picture in this correspondence to applications of stability conditions to algebraic geometry.