Generalised Beauville Groups

TL;DR

This paper introduces the concept of generalized Beauville groups, extending the classical notion to actions on products of multiple Riemann surfaces, and explores the minimal number of factors needed for such actions.

Contribution

It defines generalized Beauville groups for higher products of Riemann surfaces and investigates the minimal number of factors for free and faithful actions.

Findings

Defined generalized Beauville groups for d ≥ 2

Identified minimal d for free actions on product of Riemann surfaces

Extended classical Beauville group theory to higher dimensions

Abstract

A Beauville group acts freely on the product of two compact Riemann surfaces and faithfully on each one of them. In this paper, we consider higher products and present {\it{generalised Beauville groups}}: for $d \geq 2$, $d$ is the minimal value for which the same action can be defined on the product of $d$ compact Riemann surfaces.