The study reveals a one-to-one correspondence between quartic surfaces with Galois points and Eisenstein K3 surfaces, highlighting their characteristics.
We prove that there exists a one-to-one correspondence between smooth quartic surfaces with an inner Galois point and Eisenstein K3 surfaces of type (4, 3) . Furthermore, we characterize the quartic surface with 8 (the maximum number) inner Galois points as a singular K3 surface.
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Miura et al. (2025) studied this question.
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