The Galois action on Hurwitz curves

TL;DR

This paper explores how Galois groups act on Hurwitz curves and origamis, shedding light on their symmetries and algebraic properties.

Contribution

It provides new insights into the Galois actions on Hurwitz curves and origamis, connecting their geometric and algebraic structures.

Findings

Galois actions reveal symmetries of Hurwitz curves.

Connections between Hurwitz origamis and Galois groups.

Enhanced understanding of algebraic properties of these curves.

Abstract

We make some observations concerning the Galois actions on Hurwitz curves and on the closely related but lesser-known Hurwitz origamis.