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March 26, 2026Geometriae Dedicata0 citationsOpen Access

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

KMKei MiuraYamaguchi UniversitySTShingo TakiTokai University

Key Points

  • The research aims to demonstrate a correspondence between smooth quartic surfaces and K3 surfaces with specific automorphisms.
  • Proving the existence of a one-to-one correspondence
  • Characterizing quartic surfaces with multiple Galois points
  • Analyzing geometrical properties of K3 surfaces
  • Identified a correspondence between smooth quartic surfaces and K3 surfaces with order 4 automorphisms
  • Characterized quartic surfaces with two or more outer Galois points as K3 surfaces

Abstract

Abstract We prove that there exists a one-to-one correspondence between smooth quartic surfaces with an outer Galois point and K 3 surfaces with a certain automorphism of order 4. Furthermore, we characterize quartic surfaces with two or more outer Galois points as K 3 surfaces.

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Cite This Study

Miura et al. (2026) studied this question.

synapsesocial.com/papers/69c4cddcfdc3bde44891aac6https://doi.org/10.1007/s10711-026-01074-1
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Quartic surfaces with a Galois point and Eisenstein $K3$ surfaces2025 · 1 citations
  2. 2Galois points on quartic surfaces2001 · 14 citations
  3. 3K3 Surfaces2020 · 8 citations
  4. 4Field Theory for Function Fields of Plane Quartic Curves2000 · 88 citations
  5. 5On Singular K3 Surfaces1977 · 267 citations