The cohomology of the Hilbert scheme and of the compactified Jacobians of a singular curve

Friday, 27 January, 2017 - 15:45

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.

Speaker: 

Filippo Viviani

Institution: 

Università Roma Tre
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