Jordan constants for volume-preserving Cremona groups

2025/11/19 by Wang, Jiahe
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.15933

Abstract

We show that the optimal Jordan constant for the volume-preserving plane Cremona group Bir(\mathbb P², Δ) is 12. We provide a Jordan constant of 60 for the three-dimensional volume-preserving Cremona group Bir(\mathbb P³,Δ). We also provide a weak geometric Jordan constant of 288⋅ 16 for Bir(\mathbb P²).

Citations

• Jordan property for automorphism groups of compact varieties
• Birational invariants of volume preserving maps
• Quartic surfaces up to volume preserving equivalence
• Coregularity of Fano varieties
• Small quotient minimal log discrepancies
• \mathfrak S₅-equivariant syzygies for the Del Pezzo Surface of Degree 5
• The Jordan constant for Cremona group of rank 2
• The Sarkisov program for Mori fibred Calabi-Yau pairs
• Jordan groups and automorphism groups of algebraic varieties
• The dual complex of singularities
• Jordan property for Cremona groups
• A Minkowski-style bound for the order of the finite subgroups of the Cremona group of rank 2 over an arbitrary field
• Finite subgroups of the plane Cremona group
• Splitting fields of G-varieties

Related

• The Jordan constant for Cremona group of rank 2
• The Jordan property of Cremona groups and essential dimension
• Jordan property for Cremona group over a finite field
• Jordan constants of Cremona group of rank 2 over fields of characteristic zero
• Jordan property for Cremona groups