Veech groups of flat structures on Riemann surfaces

TL;DR

This paper introduces new examples of Veech groups for flat structures on Riemann surfaces, extending existing methods to cover unramified finite coverings of regular polygons and calculating their groups algebraically.

Contribution

It extends Schmithusen's method to unramified coverings of regular polygons and computes their Veech groups algebraically, providing new examples in the field.

Findings

Constructed new Veech groups for unramified coverings

Extended existing methods to broader classes of surfaces

Calculated specific Veech groups algebraically

Abstract

In this paper, we construct new examples of Veech groups by extending Schmithusen's method for calculating Veech groups of origamis to Veech groups of unramified finite coverings of regular 2n-gons. We calculate the Veech groups of certain Abelian coverings of regular 2n-gons by using an algebraic method.