Wall-crossing equivalences for hypertoric varieties from hyperplane arrangements induce a braid group action on their bounded derived category of coherent sheaves via a functor from the Deligne groupoid.
Mukai,Duality betweenD(X)andD( bX)with its application to Picard sheaves, Nagoya Math
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Braid Group Action on $D^b(\mathfrak{M}_{\eta})$
Wall-crossing equivalences for hypertoric varieties from hyperplane arrangements induce a braid group action on their bounded derived category of coherent sheaves via a functor from the Deligne groupoid.