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- Title
Applications of a theorem of Singerman about Fuchsian groups.
- Authors
Antonio Costa; Hugo Parlier
- Abstract
Abstract. 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.
- Subjects
RIEMANN surfaces; MATHEMATICAL functions; FUCHSIAN groups; JACOBI varieties
- Publication
Archiv der Mathematik, 2008, Vol 91, Issue 6, p536
- ISSN
0003-889X
- Publication type
Article
- DOI
10.1007/s00013-008-2817-3