Perverse sheaves on hyperplane arrangements and gluing


A hyperplane arrangement cuts up a vector space into several pieces. The combinatorics and topology of this subdivision is encoded in the associated abelian category of perverse sheaves. This category has an alternate algebraic description due to Kapranov and Schechtman, in terms of representations of a quiver with relations. I will first explain this description and some further simplifications. I will then focus on gluing, or "recollement", which is a recipe to reconstruct the category of perverse sheaves on a space from an open subset and its complement. I will describe how recollement on the above category of perverse sheaves translates to the category of quiver representations.


  •  Asilata Bapat
    Asilata Bapat, Australian National University