Cohomological invariants of genus three hyperelliptic curves

TL;DR

This paper computes the cohomological invariants with finite coefficients for the moduli stack of genus three hyperelliptic curves, advancing understanding of their algebraic and geometric properties.

Contribution

It provides the first explicit calculation of cohomological invariants for the stack of genus three hyperelliptic curves over algebraically closed fields.

Findings

Explicit cohomological invariants for genus three hyperelliptic curves

New methods for computing invariants of algebraic stacks

Enhanced understanding of the structure of hyperelliptic curve moduli

Abstract

We compute the cohomological invariants with coefficients in $\mathbb{Z}/p\mathbb{Z}$ of the stack $\mathscr{H}_3$ of hyperelliptic curves of genus $3$ over an algebraically closed field.