Fields of Moduli of Smooth Cubic Surfaces

Tianzhi Yang

Fields of Moduli of Smooth Cubic Surfaces

Algebraic Geometry 2026-07-17 v1

Authors: Tianzhi Yang

Abstract

The field of moduli of a variety $X$ over an algebraically closed field $K$ is defined as the fixed field of those automorphisms $\sigma$ of $K$ for which $X\simeq X^{\sigma}$ . A fundamental question is under what conditions a variety admits a model over its field of moduli. We show that, in characteristic $0$ , every smooth cubic surface has a model over its field of moduli.

Keywords

field of moduli smooth cubic surface model over field of moduli algebraically closed field characteristic zero

Cite

@article{arxiv.2607.16519,
  title  = {Fields of Moduli of Smooth Cubic Surfaces},
  author = {Tianzhi Yang},
  journal= {arXiv preprint arXiv:2607.16519},
  year   = {2026}
}