Finite subgroups of the plane Cremona group

TL;DR

This paper completes the classification of finite subgroups within the group of birational transformations of the complex projective plane, advancing understanding of their conjugacy classes.

Contribution

It provides a comprehensive classification of conjugacy classes of finite subgroups in the plane Cremona group, building on and completing previous classical and modern results.

Findings

Complete classification of conjugacy classes of finite subgroups.

Identification of new conjugacy classes not previously classified.

Clarification of the structure of finite subgroups in the Cremona group.

Abstract

We complete the classical and modern work on the classification of conjugacy classes of finite subgroups of the group of birational transformations of the complex projective plane.