The Chow ring of the stack of hyperelliptic curves of odd genus

TL;DR

This paper presents a new way to describe the stack of hyperelliptic curves of odd genus as a quotient stack and computes its integral Chow ring using equivariant intersection theory.

Contribution

It introduces a novel presentation of the stack as a quotient and applies equivariant intersection theory to compute its Chow ring.

Findings

Derived a new presentation of the stack as a quotient

Computed the integral Chow ring explicitly

Applied equivariant intersection theory successfully

Abstract

We find a new presentation of the stack of hyperelliptic curves of odd genus as a quotient stack and we use it to compute its integral Chow ring by means of equivariant intersection theory.