Cohomological invariants of hyperelliptic curves of even genus

TL;DR

This paper computes the cohomological invariants with finite coefficients of the moduli stacks of hyperelliptic curves of even genus over algebraically closed fields, advancing understanding of their algebraic and geometric properties.

Contribution

It provides explicit calculations of cohomological invariants for hyperelliptic curve stacks of even genus, a previously uncharted area in algebraic geometry.

Findings

Explicit invariants for hyperelliptic stacks of even genus

Enhanced understanding of the structure of these moduli stacks

Foundations for further algebraic and geometric investigations

Abstract

Let $g$ be an even positive integer, and $p$ be a prime number. We compute the cohomological invariants with coefficients in $\mathbb{Z}/p\mathbb{Z}$ of the stacks of hyperelliptic curves $\mathscr{H}_g$ over an algebraically closed field $k_0$.