Normal coverings of hyperelliptic real algebraic curves
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- by E. Bujalance, F. J. Cirre and J. M. Gamboa
- Conform. Geom. Dyn. 11 (2007), 107-127
- DOI: https://doi.org/10.1090/S1088-4173-07-00163-4
- Published electronically: July 26, 2007
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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
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Bibliographic Information
- E. Bujalance
- Affiliation: Departamento de Matemáticas Fundamentales, Facultad de Ciencias, Universidad Nacional de Educación a Distancia, Madrid, Spain
- MR Author ID: 43085
- Email: ebujalance@mat.uned.es
- F. J. Cirre
- Affiliation: Departamento de Matemáticas Fundamentales, Facultad de Ciencias, Universidad Nacional de Educación a Distancia, Madrid, Spain
- MR Author ID: 601436
- 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
- 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 - © Copyright 2007 American Mathematical Society
- Journal: Conform. Geom. Dyn. 11 (2007), 107-127
- MSC (2000): Primary 30F50; Secondary 14P25, 30F35
- DOI: https://doi.org/10.1090/S1088-4173-07-00163-4
- MathSciNet review: 2329139