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arXiv · 1310.7241

On Jacobians of curves with superelliptic components

Lubjana Beshaj·Tony Shaska·Caleb Shor
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Abstract

We investigate the decomposition of Jacobians of superelliptic curves based on their automorphisms. For curve with equation $y^n=f(x^m)$ we provide an necessary and sufficient condition in terms of $m$ and $n$ for the decomposition of the Jacobian induced by the automorphisms of the curve. Moreover, we generalize a construction in \cite{Ya} of a family of non-hyperelliptic curves $\mathcal X_{r,s} $ and determine arithmetic conditions on $r$ and $s$ that the Jacobians $\mbox{Jac} (\mathcal X_{r, s})$ decomposes.

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Lubjana Beshaj, Tony Shaska, Caleb Shor. 2014-04-03. On Jacobians of curves with superelliptic components. https://doi.org/10.1090/conm%2F629%2F12557

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