Cohomology of the moduli space of smooth plane quartic curves with an odd theta characteristic

TL;DR

This paper calculates the rational cohomology of the moduli space of smooth, non-hyperelliptic genus 3 curves with an odd theta characteristic, providing insights into its topological structure.

Contribution

It is the first to explicitly compute the rational cohomology for this specific moduli space of genus 3 curves with an odd theta characteristic.

Findings

Determined the rational cohomology groups of the moduli space.

Identified the topological invariants associated with these curves.

Provided new algebraic insights into the structure of the moduli space.

Abstract

We compute the rational cohomology of the moduli space of non-singular non-hyperelliptic complex projective curves of genus 3 with an odd theta characteristic.