Rational cohomology of the moduli space of genus 4 curves

[摘要] We compute the mixed Hodge structure on the rational cohomology of the moduli space of smooth genus 4 curves. Specifically, we prove that its Poincaré–Serre polynomial is 1 + t2u2 + t4u4 + t5u6. We show this by producing a stratification of the space, such that all strata are geometric quotients of complements of discriminants.

[学科分类] 数学（综合）