Perverse filtration for generalized Kummer varieties of fibered surfaces

Abstract

Let $A\to C$ be a proper surjective morphism from a smooth connected quasi-projective commutative group scheme of dimension 2 to a smooth curve. The construction of generalized Kummer varieties gives a proper morphism $A^{[[n]]}\to C^{((n))}$. We show that the perverse filtration associated with this morphism is multiplicative.