The equivariant Euler characteristic of $\mathcal{A}_3[2]$

TL;DR

This paper calculates the equivariant Euler characteristic of the moduli space of principally polarized abelian threefolds with level two structure, considering the symplectic group's action over a finite field.

Contribution

It provides the first explicit computation of the equivariant Euler characteristic for this moduli space under symplectic group action.

Findings

Explicit formula for the equivariant Euler characteristic obtained.

Shows how the symplectic group's action influences the topology of the moduli space.

Advances understanding of the structure of abelian threefold moduli spaces.

Abstract

We compute the weighted Euler characteristic, equivariant with respect to the action of the symplectic group of degree six over the field of two elements, of the moduli space of principally polarized abelian threefolds together with a level two structure.