Bruin, N. and Flynn, E. V. (2003) *N-covers of hyperelliptic curves.* Mathematical Proceedings of the Cambridge Philosophical Society (134). pp. 397-405. ISSN 0305-0041

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## Abstract

For a hyperelliptic curve C of genus g with a divisor class of order n=g+1, we shall consider an associated covering collection of curves D, each of genus g. We describe, up to isogeny, the Jacobian of each D via a map from D to C, and two independent maps from D to a curve of genus g(g-1)/2. For some curves, this allows covering techniques that depend on arithmetic data of number fields of smaller degree than standard 2-coverings; we illustrate this by using 3-coverings to find all Q-rational points on a curve of genus 2 for which 2-covering techniques would be impractical.

Item Type: | Article |
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Uncontrolled Keywords: | Coverings of Curves, Descent. |

Subjects: | A - C > Algebraic geometry H - N > Number theory |

Research Groups: | Number Theory Group |

ID Code: | 256 |

Deposited By: | E. Victor Flynn |

Deposited On: | 12 Jul 2006 |

Last Modified: | 20 Jul 2009 14:19 |

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