Birational transformations belonging to Galois points for a certain plane quartic

TL;DR

This paper investigates birational transformations related to Galois points on specific plane quartic curves, showing they extend to Cremona transformations and are conjugate to linear transformations.

Contribution

It characterizes the conjugacy classes of these birational transformations, revealing they are all conjugate to linear transformations, and extends them to Cremona transformations.

Findings

Transformations extend to Cremona transformations

All transformations are conjugate to linear transformations

Provides classification of these birational transformations

Abstract

In this article, we study birational transformations belonging to Galois points for certain plane quartic curve. In fact, we see that they can be extended to Cremona transformations. In particular, we determine the conjugacy class of them. We have that they are all conjugate to linear transformations.