Double coverings of hyperelliptic real algebraic curves |
| |
Authors: | E. Bujalance |
| |
Affiliation: | a Departamento de Matemáticas Fundamentales, Facultad de Ciencias, Universidad Nacional de Educación a Distancia, Madrid, Spain b Departamento de Álgebra, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Madrid, Spain |
| |
Abstract: | We consider double and (possibly) branched coverings π:X→X′ between real algebraic curves where X is hyperelliptic. 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. We first analyse the topological features and ramification data of such coverings. Second, for each isomorphism class of these coverings we then describe a representative, with defining polynomial equations for X and for X′, a formula for the involution that generates the covering transformation group, and a rational formula for the covering projection π:X→X′. |
| |
Keywords: | 14H30 30F50 |
本文献已被 ScienceDirect 等数据库收录! |
|