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On Jacobians of curves with superelliptic components

Lubjana Beshaj, Tanush Shaska, Caleb Shor

I-AIMS paper 2013-1 · Published in Contemp. Math. 629 (2014), 1–14 · 2014

We construct a family of non-hyperelliptic curves whose Jacobians decompose into a product of superelliptic Jacobians. This generalizes an earlier construction. Moreover, we investigate the decomposition of Jacobians of superelliptic curves based on their automorphisms. For a curve given by the equation yⁿ = f(xᵐ), we provide a necessary and sufficient condition in terms of m and n for the Jacobian of the curve to decompose.

MSC classes: Primary 11G10, 14K02; Secondary 11G30, 14Q05

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