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One-dimensional Hurwitz spaces, modular curves, and real forms of Belyi meromorphic functions
Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional de Educación Distancia (UNED), Senda del rey 9, 28040 Madrid, Spain.
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.ORCID iD: 0000-0002-9557-9566
Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Santiago, Chile.
2008 (English)In: International journal of mathematics and mathematical sciences, ISSN 0161-1712, Vol. 2008Article in journal (Refereed) Published
Abstract [en]

Hurwitz spaces are spaces of pairs (S, f) where S is a Riemann surface and f : S ? C^ a meromorphicfunction. In this work, we study 1-dimensional Hurwitz spaces HDp of meromorphic p-fold functions with four branched points, three of them fixed, the corresponding monodromy representation over each branched point is a product of (p - 1)/2 transpositions and the monodromy groupis the dihedral group Dp. We prove that the completion HDp of the Hurwitz space HDp is uniformized by a non-nomal index p + 1 subgroup of a triangular group with signature (0, [p, p, p]). We also establish the relation of the meromorphic covers with elliptic functions and show that HDp is aquotient of the upper half plane by the modular group G (2) n G0 (p). Finally, we study the real forms of the Belyi projection HDp ? C^ and show that there are two nonbicoformal equivalent such real forms which are topologically conjugated.

Place, publisher, year, edition, pages
2008. Vol. 2008
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-46210DOI: 10.1155/2008/609425OAI: diva2:267106
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2015-03-09

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Izquierdo, Milagros
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