Perverse filtration for generalized Kummer varieties of fibered surfaces

TL;DR

This paper proves that the perverse filtration for generalized Kummer varieties arising from fibered surfaces is multiplicative, enhancing understanding of their geometric and cohomological structure.

Contribution

It establishes the multiplicativity of the perverse filtration for generalized Kummer varieties associated with fibered surfaces, a novel result in this context.

Findings

Perverse filtration is multiplicative for these varieties.

Provides new insights into the structure of generalized Kummer varieties.

Connects geometric properties with cohomological filtrations.

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.