Archiv der Mathematik

, Volume 91, Issue 6, pp 536–543

Applications of a theorem of Singerman about Fuchsian groups


DOI: 10.1007/s00013-008-2817-3

Cite this article as:
Costa, A.F. & Parlier, H. Arch. Math. (2008) 91: 536. doi:10.1007/s00013-008-2817-3


Assume that we have a (compact) Riemann surface S, of genus greater than 2, with \(S = {\mathbb{D}}/ \Gamma\), where \({\mathbb{D}}\) is the complex unit disc and Γ is a surface Fuchsian group. Let us further consider that S has an automorphism group G in such a way that the orbifold S/G is isomorphic to \({\mathbb{D}}/\Gamma^\prime\) where \(\Gamma^\prime\) is a Fuchsian group such that \(\Gamma \vartriangleleft \Gamma^\prime\) and \(\Gamma^\prime\) has signature σ appearing in the list of non-finitely maximal signatures of Fuchsian groups of Theorems 1 and 2 in [6]. We establish an algebraic condition for G such that if G satisfies such a condition then the group of automorphisms of S is strictly greater than G, i.e., the surface S is more symmetric that we are supposing. In these cases, we establish analytic information on S from topological and algebraic conditions.

Mathematics Subject Classification (2000).

Primary 30F10 Secondary 20H10 


Riemann surface Fuchsian group orbifold 

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  1. 1.Departamento de Matemáticas FundamentalesFacultad de Ciencias, UNEDMadridSpain
  2. 2.EPFL IGAT InstituteBâtiment BCHLausanneSwitzerland

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