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

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

2004-05-22

arxiv.org/abs/math/0405427v2

Mathematics

Algebraic Geometry

12 pages, Latex; Table 5 corrected

Scientific paper

For a partition $lambda=\{lambda_1 \geq \lambda_2 \geq \lambda_3 \}$ of non-negative integers, we calculate the Euler characteristic of the local system $V_{\lambda}$ on the moduli space of genus 3 hyperelliptic curves using a suitable stratification. For some $\lambda$ of low degree, we make a guess for the motivic Euler characteristic of $V_{\lambda}$ using counting of curves over finite fields.

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