On the one-dimensional family of Riemann surfaces of genus $q$ with $4q$ automorphisms

Abstract

Bujalance, Costa and Izquierdo have recently proved that all those Riemann surfaces of genus $g\ge 2$ different from $3,6,12,15$ and 30, with exactly $4g$ automorphisms form an equisymmetric one-dimensional family, denoted by ${\mathcal{F}}_g.$ In this paper, for every prime number $q\ge 5,$ we explore further properties of each Riemann surface $S$ in ${\mathcal{F}}_q$ as well as of its Jacobian variety $JS.$

22 pages

References in corpus (8)

• Quasiplatonic curves with symmetry group ${\mathbb{Z}}_2^2⋊{\mathbb{Z}}_m$ are definable over $\mathbb{Q}$
• Fields of moduli of classical Humbert curves
• On Jacobians with group action and coverings
• A generalisation of Kani-Rosen decomposition theorem for Jacobian varieties
• On The Group Algebra Decomposition of a Jacobian Variety
• The arithmeticity of a Kodaira Fibration is determined by its universal cover
• Families of Riemann Surfaces, Uniformization and Arithmeticity
• Field of moduli of generalized Fermat curves

Cited by in corpus (8)

• A note on large automorphism groups of compact Riemann surfaces
• On Jacobians with group action and coverings
• On families of Riemann surfaces with automorphisms
• On Riemann surfaces of genus $g$ with $4g-4$ automorphisms
• On $pq$-fold regular covers of the projective line
• On large prime actions on Riemann surfaces
• Nilpotent groups of automorphisms of families of Riemann surfaces
• Abelian varieties and Riemann surfaces with generalized quaternion group action