Multiplicativity of perverse filtration for Hilbert schemes of fibered surfaces

et S → C be a smooth projective surface with numerically trivial canonical bundle fibered onto a curve. We prove the multiplicativity of the perverse filtration with respect to the cup product on H*(S[n], Q) for the natural morphism S[n] → C(n). We also prove the multiplicativity for five families of Hitchin systems obtained in a similar way and compute the perverse numbers of the Hitchin moduli spaces. We show that for small values of...