Quartic surfaces with a Galois point and Eisenstein K3 surfaces

Key Points

• A one-to-one correspondence exists between smooth quartic surfaces with Galois points and Eisenstein K3 surfaces.
• The quartic surface with 8 inner Galois points is characterized as a singular K3 surface.
• The findings enhance the understanding of the structures of both quartic surfaces and K3 surfaces.
• This work contributes significantly to the classification of quartic surfaces in algebraic geometry.