How to split two-dimensional Jacobians: a geometric construction
| Autor: | Gallese, Andrea |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $\pi\colon Y \to X$ 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. Comment: 30 pages, comments are welcome! |
| Databáze: | arXiv |
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