Cohomology of Hilbert schemes of curves with planar
singularities                                                                                         
-- Zhiwei Yun, November 11, 2011

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For a smooth curve, the Hilbert schemes of points are just
symmetric powers of the curve, and their cohomology is easily
computed in terms of H<sup>1</sup> of the curve. In joint work
with Davesh Maulik, we generalize this formula to curves with
planar singularities (as conjectured by Migliorini and
proved independently by Migliorini and Shende). In the singular
case, the compactified Jacobian will play an important role in
the formula, and our proof uses Ng&ocirc;'s technique from his proof
of the fundamental lemma.