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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
GAP
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