Rational cohomology of the moduli space of trigonal curves of genus 5

TL;DR

This paper computes the rational cohomology of the moduli space of trigonal genus 5 curves using geometric embeddings and a topological method, providing new insights into their algebraic structure.

Contribution

It introduces a novel application of Gorinov-Vassiliev's method to the moduli space of trigonal genus 5 curves, advancing understanding of their cohomological properties.

Findings

Explicit computation of the rational cohomology groups.

Identification of the topological structure of the moduli space.

Application of Hirzebruch surface embeddings to algebraic geometry.

Abstract

We compute the rational cohomology of the moduli space of trigonal curves of genus 5. We do this by considering their natural embedding in the first Hirzebruch surface and by using Gorinov-Vassiliev's method.