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

2025/04/03 by Carocca, Angel, Reyes-Carocca, Sebastián
#14H30 #14H37 #14H40 #30F10 #30F35 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.02771

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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