On Riemann surfaces of genus $g$ with $4g-4$ automorphisms

Abstract

In this article we study compact Riemann surfaces with a non-large group of automorphisms of maximal order; namely, compact Riemann surfaces of genus $g$ with a group of automorphisms of order $4g-4.$ Under the assumption that $g-1$ is prime, we provide a complete classification of them and determine isogeny decompositions of the corresponding Jacobian varieties.

15 pages

References in corpus (6)

• On the one-dimensional family of Riemann surfaces of genus $q$ with $4q$ automorphisms
• A note on large automorphism groups of compact Riemann surfaces
• Quasiplatonic curves with symmetry group ${\mathbb{Z}}_2^2⋊{\mathbb{Z}}_m$ are definable over $\mathbb{Q}$
• On Jacobians with group action and coverings
• A generalisation of Kani-Rosen decomposition theorem for Jacobian varieties
• Riemann surfaces with a large abelian group of automorphisms

Cited by in corpus (5)

• A note on large automorphism groups of compact Riemann surfaces
• On families of Riemann surfaces with 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