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 |
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2003
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| _version_ | 1826262022628573184 |
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| author | Bruin, N Flynn, E |
| author_facet | Bruin, N Flynn, E |
| author_sort | Bruin, N |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T19:29:47Z |
| format | Journal article |
| id | oxford-uuid:1d119678-e2ed-4afa-b4d3-77ec9649ccd6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:29:47Z |
| publishDate | 2003 |
| record_format | dspace |
| spelling | oxford-uuid:1d119678-e2ed-4afa-b4d3-77ec9649ccd62022-03-26T11:08:49ZN-covers of hyperelliptic curvesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1d119678-e2ed-4afa-b4d3-77ec9649ccd6EnglishSymplectic Elements at Oxford2003Bruin, NFlynn, EFor 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. |
| spellingShingle | Bruin, N Flynn, E N-covers of hyperelliptic curves |
| title | N-covers of hyperelliptic curves |
| title_full | N-covers of hyperelliptic curves |
| title_fullStr | N-covers of hyperelliptic curves |
| title_full_unstemmed | N-covers of hyperelliptic curves |
| title_short | N-covers of hyperelliptic curves |
| title_sort | n covers of hyperelliptic curves |
| work_keys_str_mv | AT bruinn ncoversofhyperellipticcurves AT flynne ncoversofhyperellipticcurves |