The orbifold cohomology of moduli of genus 3 curves

Abstract

In this work we study the additive orbifold cohomology of the moduli stack of smooth genus g curves. We show that this problem reduces to investigating the rational cohomology of moduli spaces of cyclic covers of curves where the genus of the covering curve is g. Then we work out the case of genus g=3. Furthermore, we determine the part of the orbifold cohomology of the Deligne-Mumford compactification of the moduli space of genus 3 curves that comes from the Zariski closure of the inertia stack of M_3.

29 pages, 2 figures. Minor changes, to appear in Manuscripta Math

References in corpus (4)

• The Chen-Ruan cohomology of moduli of curves of genus 2 with marked points
• Irreducibility of the space of cyclic covers of algebraic curves of fixed numerical type and the irreducible components of $Sing(\overline{{\mathfrak{M}}_g})$
• The orbifold cohomology of moduli of hyperelliptic curves
• Rational cohomology of \bar R_2 (and \bar S_2)

Cited by in corpus (1)

• The Chen-Ruan cohomology of moduli of curves of genus 2 with marked points