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arXiv · 2010.08481

A note on Jacobians of quasiplatonic Riemann surfaces with complex multiplication

Sebastián Reyes-Carocca
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Abstract

Let $m \geqslant 6$ be an even integer. In this short note we prove that the Jacobian variety of a quasiplatonic Riemann surface with associated group of automorphisms isomorphic to $C_2^2 \rtimes_2 C_m$ admits complex multiplication. We then extend this result to provide a criterion under which the Jacobian variety of a quasiplatonic Riemann surface admits complex multiplication.

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Sebastián Reyes-Carocca. 2020-10-16. A note on Jacobians of quasiplatonic Riemann surfaces with complex multiplication. https://doi.org/10.1007/s10711-020-00577-9

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