Curves of genus 2 with (n, n)-decomposable jacobians
| dc.creator | Shaska, T. | |
| dc.date | 2003-12-15 | |
| dc.date.accessioned | 2026-07-07T05:03:55Z | |
| dc.date.available | 2026-07-07T05:03:55Z | |
| dc.description | Let $C$ be a curve of genus 2 and $ψ_1:C \lar E_1$ a map of degree $n$, from $C$ to an elliptic curve $E_1$, both curves defined over $\bC$. This map induces a degree $n$ map $ϕ_1:\bP^1 \lar \bP^1$ which we call a Frey-Kani covering. We determine all possible ramifications for $ϕ_1$. If $ψ_1:C \lar E_1$ is maximal then there exists a maximal map $ψ_2:C\lar E_2$, of degree $n$, to some elliptic curve $E_2$ such that there is an isogeny of degree $n^2$ from the Jacobian $J_C$ to $E_1 \times E_2$. We say that $J_C$ is $(n,n)$-decomposable. If the degree $n$ is odd the pair $(ψ_2, E_2)$ is canonically determined. For $n=3, 5$, and 7, we give arithmetic examples of curves whose Jacobians are $(n,n)$-decomposable. | |
| dc.identifier | https://arxiv.org/abs/math/0312285 | |
| dc.identifier | http://arxiv.org/abs/math/0312285 | |
| dc.identifier | J. Symbolic Comp. 31 (2001), no. 5, 603-617 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69603 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14xx | |
| dc.title | Curves of genus 2 with (n, n)-decomposable jacobians | |
| dc.type | text |