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arXiv · 2504.02771

The locus of Riemann surfaces of genus $2(p-1)$ with $4p$ automorphisms

Angel Carocca·Sebastián Reyes-Carocca
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Abstract

Let $p \geqslant 5$ be a prime number. In this article we provide a complete and explicit description of the locus formed by the compact Riemann surfaces of genus $2(p-1)$ that are endowed with a group of automorphisms of order $4p$. In addition, we provide isogeny decompositions of the corresponding Jacobian varieties and study if the most symmetric ones admit complex and real multiplication.

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Angel Carocca, Sebastián Reyes-Carocca. 2025-04-03. The locus of Riemann surfaces of genus $2(p-1)$ with $4p$ automorphisms. https://arxiv.org/abs/2504.02771

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