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.