Autoduality of compactified Pryms for étale double covers of curves with planar singularities

Abstract

We construct a Poincaré sheaf on the compactified Prym variety associated with an étale double cover of integral curves with planar singularities, and prove that the associated Fourier-Mukai transform is an autoequivalence of its derived category. As an application, we prove the motivic decomposition conjecture of Corti-Hanamura for the Laza-Saccà-Voisin fibration, and construct a multiplicative motivic perverse filtration lifting the cohomological one.