N-covers of hyperelliptic curves
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,...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
| Published: |
2003
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| Summary: | 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. |
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