N-covers of hyperelliptic curves

Journal article

For a hyperelliptic curve script C sign of genus g with a divisor class of order n = g + 1, we shall consider an associated covering collection of curves script D signδ, each of genus g2. We describe, up to isogeny, the Jacobian of each script D signδ via a map from script D signδ to script C sign, and two independent maps from script D signδ 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.

Authors: Bruin, N; Flynn, E

• Publication status: Published
• Journal: MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
• Volume: 134
• Issue: 3
• Pages: 397-405
• Publication date: 2003-05-01
• DOI: 10.1017/S0305004102006448
• EISSN: 1469-8064
• ISSN: 0305-0041
• Language: English