Quartic surfaces with an outer Galois point and K3 surfaces with an automorphism of order 4

TL;DR

This paper establishes a correspondence between certain quartic surfaces with Galois points and K3 surfaces with specific automorphisms, providing new insights into their geometric structures and classifications.

Contribution

It introduces a novel correspondence between quartic surfaces with outer Galois points and K3 surfaces with automorphisms of order 4, and characterizes those with multiple Galois points.

Findings

One-to-one correspondence between smooth quartic surfaces with an outer Galois point and K3 surfaces with a specific automorphism.

Characterization of quartic surfaces with two or more outer Galois points as K3 surfaces.

New classification results linking Galois points and automorphisms on K3 surfaces.

Abstract

We prove that there exists a one-to-one correspondence between smooth quartic surfaces with an outer Galois point and K3 surfaces with a certain automorphism of order 4. Furthermore, we characterize quartic surfaces with two or more outer Galois points as K3 surfaces.