Galois lines for the quotient curve of the Hermitian curve by an involution

TL;DR

This paper characterizes all Galois lines for the quotient of the Hermitian curve by an involution in projective space, and identifies Galois points on related plane models, advancing understanding of algebraic curve symmetries over finite fields.

Contribution

It provides a complete description of Galois lines for the quotient curve and classifies Galois points on specific plane models, a novel geometric insight.

Findings

All Galois lines for the quotient curve are described.

Galois points for certain plane models are fully determined.

The geometric structure over finite fields is elucidated.

Abstract

The arrangement of all Galois lines for the quotient curve of the Hermitian curve by an involution in the projective 3-space is described, in terms of the geometry over finite fields. All Galois points for three plane models of this curve admitting three or more Galois points are also determined.