Conjugacy classes of linear actions in the plane Cremona group

TL;DR

This paper classifies how finite groups can act on the projective plane in a way that is both regular and generically free, up to conjugation within the Cremona group, advancing understanding of group actions in algebraic geometry.

Contribution

It provides a complete classification of finite group actions on the projective plane up to conjugation in the Cremona group, focusing on regular and generically free actions.

Findings

Classification of finite group actions on the projective plane.

Identification of conjugacy classes within the Cremona group.

Insights into the structure of the Cremona group.

Abstract

We classify regular generically free actions of finite groups on the projective plane, up to conjugation in the Cremona group.