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A note on Jacobians of quasiplatonic Riemann surfaces with complex multiplication
Geometriae Dedicata ( IF 0.5 ) Pub Date : 2020-11-17 , DOI: 10.1007/s10711-020-00577-9
Sebastián Reyes-Carocca

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.

中文翻译:

关于复数乘法拟柏拉图黎曼曲面的雅可比矩阵的注记

令 $m \geqslant 6$ 为偶数。在这个简短的注释中,我们证明了具有同构于 $C_2^2 \rtimes_2 C_m$ 的相关自同构群的拟柏拉图黎曼曲面的雅可比变体承认复数乘法。然后我们扩展这个结果以提供一个标准,在该标准下准柏拉图黎曼曲面的雅可比变体允许复数乘法。
更新日期:2020-11-17
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