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Decomposing Jacobians of curves with extra automorphisms. (English) Zbl 1142.14017
The author studies the decomposition up to isogeny of the Jacobian of certain curves up to genus \(10\). The aim is to obtain examples of Jacobian isogenous to a copy of an elliptic curve for each genus. This goal is reached in the case \(g \leq 6\) and partly for \(7 \leq g \leq 10\). To obtain these decompositions, the author considers curves with many automorphisms and uses two important results obtained by E. Kani and M. Rosen [Math. Ann. 284, No. 2, 307–327 (1989; Zbl 0652.14011)], combined with the Riemann-Hurwitz theorem and the research of idempotents thanks to the explicit description of the group of automorphisms \(G\) of certain curves \(X\) and the monodromy of the cover \(X \to X/G\).

MSC:
14H40 Jacobians, Prym varieties
14H45 Special algebraic curves and curves of low genus
11G05 Elliptic curves over global fields
14H37 Automorphisms of curves
Software:
GAP
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