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

Abstract

For a partition λ ={ λ1 ≥ λ2 ≥ λ3 ≥ 0} of non-negative integers, we calculate the Euler characteristic of the local system Vλ 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 Vλ using counting curves over finite fields. Mathematics Subject Classification (1991): 14J15, 20B25