How to split two-dimensional Jacobians: a geometric construction
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912192989757440 |
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| author | Gallese, Andrea |
| author_facet | Gallese, Andrea |
| contents | Let $π\colon Y \to X$ be a branched cover of complex algebraic curves of respective genera $g(Y)=2$ and $g(X)=1$. The Jacobian of $Y$ is isogenous to the product of two elliptic curves: $\operatorname{Jac} Y \sim \operatorname{Jac} X \times \operatorname{Jac} W$. We present an explicit geometric construction of the complementary curve $W$. Furthermore, we establish a criterion to decide whether an algebraic correspondence of curves admits a push-out. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07414 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | How to split two-dimensional Jacobians: a geometric construction Gallese, Andrea Algebraic Geometry 14H30, 14H40 (Primary), 14K20, 14Q05, 57M12, 37F20 (Secondary) Let $π\colon Y \to X$ be a branched cover of complex algebraic curves of respective genera $g(Y)=2$ and $g(X)=1$. The Jacobian of $Y$ is isogenous to the product of two elliptic curves: $\operatorname{Jac} Y \sim \operatorname{Jac} X \times \operatorname{Jac} W$. We present an explicit geometric construction of the complementary curve $W$. Furthermore, we establish a criterion to decide whether an algebraic correspondence of curves admits a push-out. |
| title | How to split two-dimensional Jacobians: a geometric construction |
| topic | Algebraic Geometry 14H30, 14H40 (Primary), 14K20, 14Q05, 57M12, 37F20 (Secondary) |
| url | https://arxiv.org/abs/2412.07414 |