Rational cohomology of the moduli space of genus 4 curves

By O. Tommasi. Compositio Mathematica, 2003

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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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2ba7309ea503adc5b34bd433e6a5c181d65148ab