2026-04-17T11:38:37Zhttps://recercat.cat/oai/requestoai:recercat.cat:2445/2226062025-12-05T01:47:57Zcom_2072_1057col_2072_478917col_2072_478920
RECERCAT
author
Naranjo del Val, Juan Carlos
author
Ortega Ortega, Angela
author
Spelta, Irene
2025-07-28T08:22:37Z2025-07-28T08:22:37Z2024-05-212025-07-28T08:22:37Z
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.
cc-by (c) J.C. Naranjo et al., 2024 http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess
Formes de Jacobi
Varietats abelianes
Corbes algebraiques
Jacobi forms
Abelian varieties
Algebraic curves
Cyclic coverings of genus 2 curves of Sophie Germain type
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion