An analog of the Edwards model for Jacobians of genus 2 curves
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911813614960640 |
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| author | Flynn, E. Victor Khuri-Makdisi, Kamal |
| author_facet | Flynn, E. Victor Khuri-Makdisi, Kamal |
| contents | We give the explicit equations for a P^3 x P^3 embedding of the Jacobian of a curve of genus 2, which gives a natural analog for abelian surfaces of the Edwards curve model of elliptic curves. This gives a much more succinct description of the Jacobian variety than the standard version in P^{15}. We also give a condition under which, as for the Edwards curve, the abelian surfaces have a universal group law. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_01450 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | An analog of the Edwards model for Jacobians of genus 2 curves Flynn, E. Victor Khuri-Makdisi, Kamal Number Theory Symbolic Computation Algebraic Geometry 11G30, 11G10, 14H40 We give the explicit equations for a P^3 x P^3 embedding of the Jacobian of a curve of genus 2, which gives a natural analog for abelian surfaces of the Edwards curve model of elliptic curves. This gives a much more succinct description of the Jacobian variety than the standard version in P^{15}. We also give a condition under which, as for the Edwards curve, the abelian surfaces have a universal group law. |
| title | An analog of the Edwards model for Jacobians of genus 2 curves |
| topic | Number Theory Symbolic Computation Algebraic Geometry 11G30, 11G10, 14H40 |
| url | https://arxiv.org/abs/2211.01450 |