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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/224822
Families of simple Jacobians with many automorphisms
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We study an explicit ( $2 g-1$ )-dimensional family of Jacobian varieties of dimension $\frac{1}{2}(d-1)(g-1)$, arising from quotient curves of unramified cyclic coverings of prime degree $d$ of hyperelliptic curves of genus $g \geqslant 2$. By using a deformation argument, we prove that the generic element of the family is simple. Furthermore, we completely describe their endomorphism algebra, and we show that they admit a rank $\frac{1}{2}(d-1)-1$ group of non-polarized automorphisms. As an application of these results, we prove the generic injectivity of the Prym map for étale cyclic coverings of hyperelliptic curves of odd prime degree under some slight numerical restrictions. This result generalizes in several directions previous results on genus 2 .
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NARANJO DEL VAL, Juan Carlos, et al. Families of simple Jacobians with many automorphisms. Algebraic Geometry. 2025. Vol. 12, num. 6, pags. 869-887. ISSN 2214-2584. [consulted: 15 of June of 2026]. Available at: https://hdl.handle.net/2445/224822