On the connectedness of the branch locus of the moduli space of Riemann surfaces of low genus
2012 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 140, no 1, 35-45 p.Article in journal (Refereed) Published
Let be an integer and let , where denotes the moduli space of compact Riemann surfaces of genus . Using uniformization of Riemann surfaces by Fuchsian groups and the equisymmetric stratification of the branch locus of the moduli space, we prove that the subloci corresponding to Riemann surfaces with automorphism groups isomorphic to cyclic groups of order 2 and 3 belong to the same connected component. We also prove the connectedness of for and with the exception of the isolated points given by Kulkarni.
Place, publisher, year, edition, pages
American Mathematical Society , 2012. Vol. 140, no 1, 35-45 p.
Moduli spaces, Teichmüller modular group, automorphism group
National CategoryNatural Sciences
IdentifiersURN: urn:nbn:se:liu:diva-73196DOI: 10.1090/S0002-9939-2011-10881-5ISI: 000299596000004OAI: oai:DiVA.org:liu-73196DiVA: diva2:468692
FunderSwedish Research Council