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Manuscripta Mathematica

, Volume 142, Issue 3–4, pp 409–437 | Cite as

The orbifold cohomology of moduli of genus 3 curves

  • N. Pagani
  • O. TommasiEmail author
Article

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 \({\mathcal{M}3}\) .

Mathematics Subject Classifications (2010)

Primary: 14H10 55N32 Secondary: 14N35 14D23 14H37 32G15 55P50 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institut für Algebraische GeometrieLeibniz Universität HannoverHannoverGermany

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