The orbifold cohomology of moduli of hyperelliptic curves
Abstract
We study the inertia stack of [M0,n/Sn], the quotient stack of the moduli space of smooth genus 0 curves with n marked points via the action of the symmetric group Sn. Then we see how from this analysis we can obtain a description of the inertia stack of Hg, the moduli stack of hyperelliptic curves of genus g. From this, we can compute additively the Chen-Ruan (or orbifold) cohomology of Hg.
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