A new characterisation of the Fermat curve

Abstract

This paper presents a new characterisation of the Fermat curve, according to the arrangement of Galois points.

arXiv comment14 pages. In the second version, the proof for the case where the degree $d$ of the curve is six was added, and the assumption $d\ne 6$ in Theorem was removed. In the third version, the proof for the case $d=4$ was revised