A Minkowski-style bound for the order of the finite subgroups of the Cremona group of rank 2 over an arbitrary field

2009/03/03 by Serre, Jean-Pierre · 3 citations
#14E07 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0903.0514

Abstract

Let Cr(k) be the Cremona group of rank 2 over a field k, i.e. the group of all k-automorphisms of k(X,Y). We determine the l.c.m. of the orders of the finite subgroups of Cr(k) of order prime to the characteristic of k.

Cited by

• ML-invariant and automorphism groups of certain word varieties in SL(2,C)²
• Jordan bounds for volume-preserving Cremona groups
• Representations of finite subgroups of Cremona groups

Related

• Bounds for the order for p-elementary subgroups in the plane Cremona group over a perfect field
• Finite subgroups of maximal order of the Cremona group over the rationals
• Jordan property for Cremona group over a finite field
• On elements of order p^s in the plane Cremona group over a field of characteristic p
• On finite subgroups of Cremona group of rank 2 in odd characteristic