Bujalance, E. and Cirre, F.J. and Gamboa, J. M. (2007) Normal coverings of hyperelliptic real algebraic curves. Conformal geometry and dynamics, 11 . pp. 107127. ISSN 10884173

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Official URL: http://www.ams.org/journals/ecgd/20071109/S1088417307001634/S1088417307001634.pdf
Abstract
We consider normal (possibly) branched, finitesheeted coverings $ \pi:X\rightarrow X'$ between hyperelliptic real algebraic curves. We are interested in the topology of such coverings and also in describing them in terms of algebraic equations. In this article we completely solve these two problems in case $ X$ has the maximum number of ovals within its genus. We first analyze the topological features and ramification data of such coverings. For each isomorphism class we then describe a representative, with defining polynomial equations for $ X$ and for $ X'$, formulae for generators of the covering transformation group, and a rational formula for the covering $ \pi:X\rightarrow X'$.
Item Type:  Article 

Uncontrolled Keywords:  Klein surfaces; Topology of real algebraic varieties; Fuchsian groups and automorphic functions 
Subjects:  Sciences > Mathematics > Algebra 
ID Code:  17274 
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