A note on large automorphism groups of compact Riemann surfaces

Abstract

Belolipetsky and Jones classified those compact Riemann surfaces of genus $g$ admitting a large group of automorphisms of order $\lambda (g-1)$, for each $\lambda >6,$ under the assumption that $g-1$ is a prime number. In this article we study the remaining large cases; namely, we classify Riemann surfaces admitting $5(g-1)$ and $6(g-1)$ automorphisms, with $g-1$ a prime number. As a consequence, we obtain the classification of Riemann surfaces admitting a group of automorphisms of order $3(g-1)$, with $g-1$ a prime number. We also provide isogeny decompositions of their Jacobian varieties.

arXiv comment12 pages, To appear in Journal of Algebra

References in corpus (7)

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

Cited by in corpus (5)

• 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