Autoduality of compactified Pryms for \'etale double covers of curves with planar singularities
We construct a Poincar\'e sheaf on the compactified Prym variety associated with an \'etale 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-Sacc\`a-Voisin fibration, and construct a multiplicative motivic perverse filtration lifting the cohomological one.
math.AG↗