Perverse Schobers and Wall Crossing
Perverse Schobers and Wall Crossing
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反常的斯科伯斯和穿越墙
DOI：
10.1093/imrn/rnx280
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发表时间：
2017
影响因子：
1
通讯作者：
Donovan W
中科院分区：
文献类型：
--
作者：
Y. Miyatake;G. Eom;T. Sogabe;S.-L. Zhang;Hideaki Ikoma;Donovan Will;Hideaki Ikoma;Donovan W
对于几何不变量理论（GIT）中的平衡壁交叉口，在满足一定数值条件的情况下，相应的GIT商之间存在推导等价。给定这样一个墙交叉，我在一个磁盘上构造了一个反常的类别束，在一点上是奇异的，半单态恢复这些等价，并且在奇点上的行为由与墙相关的GIT商堆栈控制。取复化的Grothendieck群给出了一个反常的向量空间束：我描述了当它是穿孔盘上局部系统的交上同复时的特征。
For a balanced wall crossing in geometric invariant theory (GIT), 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 characterize when this is an intersection cohomology complex of a local system on the punctured disk.