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One-Dimensional Hurwitz Spaces, Modular Curves, and Real Forms of Belyi Meromorphic Functions
Joint Authors
Izquierdo, Milagros
Costa, Antonio F.
Riera, Gonzalo
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2008, Issue 2008 (31 Dec. 2008), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2008-12-17
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
Hurwitz spaces are spaces of pairs (S,f) where S is a Riemann surface and f:S→ℂ^ a meromorphic function.
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 group is 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 a quotient of the upper half plane by the modular group Γ(2)∩Γ0(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.
American Psychological Association (APA)
Costa, Antonio F.& Izquierdo, Milagros& Riera, Gonzalo. 2008. One-Dimensional Hurwitz Spaces, Modular Curves, and Real Forms of Belyi Meromorphic Functions. International Journal of Mathematics and Mathematical Sciences،Vol. 2008, no. 2008, pp.1-18.
https://search.emarefa.net/detail/BIM-484841
Modern Language Association (MLA)
Costa, Antonio F.…[et al.]. One-Dimensional Hurwitz Spaces, Modular Curves, and Real Forms of Belyi Meromorphic Functions. International Journal of Mathematics and Mathematical Sciences No. 2008 (2008), pp.1-18.
https://search.emarefa.net/detail/BIM-484841
American Medical Association (AMA)
Costa, Antonio F.& Izquierdo, Milagros& Riera, Gonzalo. One-Dimensional Hurwitz Spaces, Modular Curves, and Real Forms of Belyi Meromorphic Functions. International Journal of Mathematics and Mathematical Sciences. 2008. Vol. 2008, no. 2008, pp.1-18.
https://search.emarefa.net/detail/BIM-484841
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-484841