Quartic surfaces with a Galois point and Eisenstein K3 surfaces

Kei Miura; Shingo Taki

Quartic surfaces with a Galois point and Eisenstein K3 surfaces

Algebraic Geometry 2023-11-29 v2

Authors: Kei Miura , Shingo Taki

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.

Keywords

algebraic surfaces del pezzo surfaces cubic fourfolds

Cite

@article{arxiv.2308.11102,
  title  = {Quartic surfaces with a Galois point and Eisenstein K3 surfaces},
  author = {Kei Miura and Shingo Taki},
  journal= {arXiv preprint arXiv:2308.11102},
  year   = {2023}
}

Comments

10 pages

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