The Euler characteristic of local systems on the moduli of genus 3 hyperelliptic curves

Abstract

For a partition $lambda=\{lambda_1 \geq λ_2 \geq λ_3 \}$ of non-negative integers, we calculate the Euler characteristic of the local system $V_λ$ on the moduli space of genus 3 hyperelliptic curves using a suitable stratification. For some $λ$ of low degree, we make a guess for the motivic Euler characteristic of $V_λ$ using counting of curves over finite fields.