L. Migliorini: Support theorems for the relative Hilbert scheme of a family of planar curves

Abstract: In the first part I will discuss an analogue of Ngo's support theorem for the relative Hilbert scheme of a family of irreducible planar curves, which gives as a corollary a "MacDonald's formula for singular curves", relating the cohomology of the Hilbert scheme of a singular integral plane curve to the cohomology of its compactified Jacobian. Then I will discuss what happens for reducible (but reduced) planar curves. The first part is work in collaboration with V.Shende, the second is work in progress with V.Shende and F.Viviani.