One-dimensional Hurwitz spaces, modular curves, and real forms of Belyi meromorphic functions
2008 (English)In: International journal of mathematics and mathematical sciences, ISSN 0161-1712, Vol. 2008Article in journal (Refereed) Published
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
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-46210DOI: 10.1155/2008/609425OAI: oai:DiVA.org:liu-46210DiVA: diva2:267106