We generalize the classical MacDonald formula for smooth curves to reduced curves with planar singul
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 the weight polynomials of the spaces involved can be computed in terms of the underlying dual graph. This is a joint work with Luca Migliorini and Vivek Schende.

Date and Venue

Start Date

Speaker

Filippo Viviani

Speaker's Institution

Università Roma Tre

Area

Geometry and Topology