Riemann surfaces of genus $1+q^2$ with $3q^2$ automorphisms

TL;DR

This paper classifies certain genus $1+q^2$ Riemann surfaces with specific automorphism groups and explores their Jacobian decompositions, advancing understanding of their symmetries and algebraic structures.

Contribution

It provides a classification of genus $1+q^2$ Riemann surfaces with automorphism group order $3q^2$ and investigates their Jacobian variety decompositions.

Findings

Classification of surfaces with specified automorphism groups

Descriptions of Jacobian variety decompositions

Insights into symmetries of high-genus Riemann surfaces

Abstract

In this article we classify compact Riemann surfaces of genus $1+q^2$ with a group of automorphisms of order $3q^2,$ where $q$ is a prime number. We also study decompositions of the corresponding Jacobian varieties.