Perverse schobers and wall crossing

2017/03/02 by Donovan, W.
#14L24 #18E30 #32S60 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14F05 #Representation Theory (math.RT) #Secondary 14E05

paper · doi:10.48550/arxiv.1703.00592

Abstract

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.

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