Cohomological invariants of the stack of hyperelliptic curves of odd genus

TL;DR

This paper calculates the cohomological invariants of the moduli stack of smooth hyperelliptic curves for all odd genera, providing new insights into their algebraic structure.

Contribution

It introduces explicit computations of cohomological invariants for the entire class of hyperelliptic curve stacks of odd genus, a previously unresolved problem.

Findings

Explicit cohomological invariants for all odd genus hyperelliptic stacks

New algebraic descriptions of hyperelliptic moduli spaces

Enhanced understanding of the structure of hyperelliptic curve stacks

Abstract

We compute the cohomological invariants of $\mathcal{H}_g$, the moduli stack of smooth hyperelliptic curves, for every odd $g$.