Conjugacy classes of linear actions in the plane Cremona group

2025/08/13 by Cheltsov, Ivan, Tschinkel, Yuri, Zhang, Zhijia
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.09929

Abstract

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

Citations

• Equivariant birational geometry of linear actions
• Equivariant Burnside groups and representation theory
• Symbols and equivariant birational geometry in small dimensions
• Equivariant birational types and Burnside volume
• Finite subgroups of PGL(2,K)
• Finite subgroups of the plane Cremona group
• On planar Cremona maps of prime order
• Birational involutions of P²

Related

• The conjugacy classes of finite nonsolvable subgroups in the plane Cremona group
• Finite subgroups of the plane Cremona group
• Finite abelian subgroups of the Cremona group of the plane
• On linearization problems in the plane Cremona group
• Linearization problem for finite subgroups of the plane Cremona group