Groups acting on cubic surfaces in characteristic zero

TL;DR

This paper classifies automorphism groups of smooth cubic surfaces over fields of characteristic zero, including those acting on rational, stably rational, or unirational surfaces, providing a comprehensive group action analysis.

Contribution

It uniquely determines the automorphism groups of smooth cubic surfaces over characteristic zero fields and their actions on various rationality classes.

Findings

Classification of automorphism groups for smooth cubic surfaces

Identification of groups acting on rational, stably rational, or unirational surfaces

Comprehensive analysis of group actions in characteristic zero

Abstract

For every field $k$ of characteristic zero, we determine the groups that act as automorphisms on a smooth cubic surface over $k$. We also determine the groups that act on $k$-rational, stably $k$-rational, or $k$-unirational smooth cubic surfaces.