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Perverse Schobers and Wall Crossing
International Mathematics Research Notices ( IF 1.452 ) Pub Date : 2017-12-09 , DOI: 10.1093/imrn/rnx280
Donovan W.

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.
更新日期:2020-01-04

 

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