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Perverse schobers and wall crossing

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arxiv 1703.00592 v2 pith:I5DEPCIU submitted 2017-03-02 math.AG math.RT

W. Donovan This is my paper · ORCID
classification math.AGmath.RT
keywords wallcrossingperversediskequivalencespointsheafsingular
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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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  1. A class of perverse schobers in Geometric Invariant Theory

    math.AG 2019-08 accept novelty 7.0 of 10

    For any quasi-symmetric representation of a reductive group, the derived categories of GIT quotients form a perverse schober on the partial compactification of the stringy Kähler moduli space.

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