The Mathematical Institute, University of Oxford, Eprints Archive

N-covers of hyperelliptic curves

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$_\delta$, each of genus g$^2$. We describe, up to isogeny, the Jacobian of each D$_\delta$ via a map from D$_\delta$ to C, and two independent maps from D$_\delta$ 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
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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