The cohomology of the Hilbert scheme and of the compactified Jacobians of a singular curve
    Speaker: 
  
  
  
      Filippo Viviani, Roma Tre University  
Date and Time: 
Thursday, December 8, 2016 - 11:00am to 12:00pm
Location: 
Fields Institute, Room 230
Abstract: 
We generalize the classical MacDonald formula for smooth curves to reduced curves with planar singularities. More precisely, we show that the cohomologies of the Hilbert schemes of points on a such a curve are encoded in the cohomologies of the fine compactified Jacobians of its connected subcurves, via the perverse Leray filtration. A crucial step in the proof is the case of nodal curves, where everything reduces to some combinatorial identities on the underlying dual graph. This is a joint work with Luca Migliorini and Vivek Schende.

