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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.20 n.1 Antofagasta mayo 2001 



Universidad Técnica Federico Santa María-Chile    


In this note we consider pairs (S, T), where S is a closed Riemann surface of genus five and T : S ®   S in some anticonformal involution with fixed points so that K(S, T) = {h Î  Aut±(S) :  hT =  Th} has the maximal order 96 and S /TT  is orientable.  We observe that there are exactly two topologically different choices for T. They give non-isomorphic groups K(S,T), each one acting topologically rigid on the respective surface S. These two cases give then two (connect) real algebraic sets of real dimension one in the moduli space of genus 5. In this note we describe these components by classical Schottky groups and with the help of these uniformizations we compute their Riemann matrices.

Keywords: Schottky groups, Riemann surfaces, Riemann matrices.

Subjclass: Primary 30F40.
*Partially supported by projects UTFSM 12.01.22, Fondecyt 1000715 and a Presidential Chair on Geometry.  



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Received: November 2000.

Rubén A. Hidalgo
Departamento de Matemática
Universidad Técnica Federico Santa María

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