For a balanced wall crossing in geometric invariant theory, there exist derived equivalences between the corresponding GIT quotients if certain numerical conditions are satisfied. Given such a wall crossing, I construct a perverse sheaf of categories on a disk, singular at a point, with half-monodromies recovering these equivalences, and with behaviour at the singular point controlled by a GIT quotient stack associated to the wall. Taking complexified Grothendieck groups gives a perverse sheaf of vector spaces: I characterise when this is an intersection cohomology complex of a local system on the punctured disk.

中文翻译：

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不正常的 Schobers 和穿墙

对于几何不变理论中的平衡壁交叉，如果满足某些数值条件，则相应的 GIT 商之间存在导出的等价关系。考虑到这样的墙交叉，我在磁盘上构建了一个反常的类别束，在一点上是奇异的，半单峰恢复这些等价，并且奇异点处的行为由与墙相关联的 GIT 商堆栈控制。取复杂的 Grothendieck 群给出了一组反常的向量空间：我刻画了当这是穿孔圆盘上局部系统的交集上同调复合体时的特征。