The orbifold cohomology of moduli of hyperelliptic curves (Q2889563)

The author studies the inertia stack of \(\mathcal{M}_{0,n}\slash S_{n}\), the quotient stack of the moduli space of smooth, genus 0 curves with \(n\) marked points via symmetric group action. Then, the author obtains a description of the inertia stack of \(\mathcal{H}_{g}\), moduli stack of hyperelliptic curves of genus \(g\). One of the main results of the paper is to give a closed formula for the orbifold Poincaré polynomial of \(\mathcal{H}_{g}\) for any \(g\). The orbifold cohomology of \(\mathcal{H}_{g}\) is also computed.