Perversity equals weight for Painlevé systems


We compare two filtrations on the cohomology spaces of a finite family of smooth manifolds,
known as the Painlevé family. One of these filtrations is the perverse Leray filtration
associated to the Hitchin map on an irregular Dolbeault moduli space, the other one is the
weight filtration on the associated Betti space. We find that the dimensions of the associated
graded pieces of these two filtrations agree (up to a shift of the indices), as predicted by a
conjecture of de Cataldo, Hausel and Migliorini.