Quartic surfaces with a Galois point and Eisenstein K3 surfaces

2023/08/22 by Kei Miura, Miura, Kei, Shingo Taki +1
Mathematics · #14J50 #14J70 (Primary) 14J28 #14N05 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2308.11102

openalex publication_date 2023/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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