On stable conjugacy of finite subgroups of the plane Cremona group, II

TL;DR

This paper investigates the conditions under which finite subgroups of the plane Cremona group are linearizable, showing that stable linearizability generally implies linearizability with few exceptions.

Contribution

It establishes that, aside from specific cases, stable linearizability of finite subgroups in the Cremona group leads to their linearizability, advancing understanding of their structure.

Findings

Stable linearizability mostly implies linearizability.

Identifies exceptions where the implication does not hold.

Contributes to classification of finite subgroups in Cremona groups.

Abstract

We prove that, except for a few cases, stable linearizability of finite subgroups of the plane Cremona group implies linearizability.