Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Gold Open Access
Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

 

Normal coverings of hyperelliptic real algebraic curves


Authors: E. Bujalance, F. J. Cirre and J. M. Gamboa
Journal: Conform. Geom. Dyn. 11 (2007), 107-127
MSC (2000): Primary 30F50; Secondary 14P25, 30F35
Published electronically: July 26, 2007
MathSciNet review: 2329139
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider normal (possibly) branched, finite-sheeted 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'$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2000): 30F50, 14P25, 30F35

Retrieve articles in all journals with MSC (2000): 30F50, 14P25, 30F35


Additional Information

E. Bujalance
Affiliation: Departamento de Matemáticas Fundamentales, Facultad de Ciencias, Universidad Nacional de Educación a Distancia, Madrid, Spain
Email: ebujalance@mat.uned.es

F. J. Cirre
Affiliation: Departamento de Matemáticas Fundamentales, Facultad de Ciencias, Universidad Nacional de Educación a Distancia, Madrid, Spain
Email: jcirre@mat.uned.es

J. M. Gamboa
Affiliation: Departamento de Álgebra, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Madrid, Spain
Email: jmgamboa@mat.ucm.es

DOI: http://dx.doi.org/10.1090/S1088-4173-07-00163-4
PII: S 1088-4173(07)00163-4
Keywords: Normal coverings, hyperelliptic real algebraic curves, combinatorial methods.
Received by editor(s): February 6, 2007
Published electronically: July 26, 2007
Additional Notes: The research of the first two authors was partially supported by MEC-DGESIC (Spain) through Project MTM2005-01637.
The research of the third author was partially supported by MEC-DGESIC (Spain) through Project MTM2005-20865
Article copyright: © Copyright 2007 American Mathematical Society