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On the orbifold structure of the moduli space of Riemann surfaces of genera four and five

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Abstract

The moduli space \(\mathcal M _{g}\), of compact Riemann surfaces of genus \(g\) has orbifold structure since \(\mathcal M _{g}\) is the quotient space of the Tiechmüller space by the action of the mapping class group. Using uniformization of Riemann surfaces by Fuchsian groups and the equisymmetric stratification of the branch locus of the moduli space we find the orbifold structure of the moduli spaces of Riemann surfaces of genera 4 and 5.

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Acknowledgments

A. F. Costa is partially supported by MTM2011-23092. M. Izquierdo is partially supported by the Swedish Research Council (VR). The results on genus \(5\) are part of Bartolini’s Liccentiate Thesis. The authors are grateful to the referees for helpful comments.

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Authors and Affiliations

  1. Matematiska institutionen, Linköpings universitet, 581 83 , Linköping, Sweden

    Gabriel Bartolini & Milagros Izquierdo

  2. Departamento de Matematicas, UNED, 28040 , Madrid, Spain

    Antonio F. Costa

Authors
  1. Gabriel Bartolini
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  2. Antonio F. Costa
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  3. Milagros Izquierdo
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Correspondence to Antonio F. Costa.

Appendix: GAP-codes

Appendix: GAP-codes

Some GAP-codes to find and classify actions of groups on Riemann surfaces, beginning with a code to find admissible signatures.

figure a

Next one finds and classifies group actions with signature \((0;m_{1},\dots ,m_{k})\). A slightly modified code is used when \(g=1\).

figure b
figure c

To calculate the signatures of subgroups of Fuchsian groups:

figure d

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Bartolini, G., Costa, A.F. & Izquierdo, M. On the orbifold structure of the moduli space of Riemann surfaces of genera four and five. RACSAM 108, 769–793 (2014). https://doi.org/10.1007/s13398-013-0140-8

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  • DOI: https://doi.org/10.1007/s13398-013-0140-8

Keywords

Mathematics Subject Classificcation

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