2026-04-14T04:30:25Zhttps://recercat.cat/oai/request

oai:recercat.cat:2445/2226062025-12-05T01:47:57Zcom_2072_1057col_2072_478917col_2072_478920

00925njm 22002777a 4500 dc Naranjo del Val, Juan Carlos author Ortega Ortega, Angela author Spelta, Irene author 2025-07-28T08:22:37Z 2025-07-28T08:22:37Z 2024-05-21 2025-07-28T08:22:37Z We consider cyclic unramified coverings of degree $d$ of irreducible complex smooth genus 2 curves and their corresponding Prym varieties. They provide natural examples of polarized abelian varieties with automorphisms of order $d$. The rich geometry of the associated Prym map has been studied in several papers, and the cases $d=2,3,5,7$ are quite well understood. Nevertheless, very little is known for higher values of $d$. In this paper, we investigate whether the covering can be reconstructed from its Prym variety, that is, whether the generic Prym Torelli theorem holds for these coverings. We prove this is so for the so-called Sophie Germain prime numbers, that is, for $d \geq 11$ prime such that $\frac{d-1}{2}$ is also prime. We use results of arithmetic nature on $G L_2$-type abelian varieties combined with theta-duality techniques. Formes de Jacobi Varietats abelianes Corbes algebraiques Jacobi forms Abelian varieties Algebraic curves Cyclic coverings of genus 2 curves of Sophie Germain type