A Minkowski-style Bound for the Orders of the Finite Subgroups of the Cremona Group of Rank 2 over an Arbitrary Field

2009/01/01 by Jean-Pierre Serre · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Analytic Number Theory Research #Mathematics #Rank (graph theory) #Minkowski space #Group (periodic table) #Field (mathematics) #Combinatorics #Style (visual arts) #Pure mathematics #Geometry #Geography #Physics #Archaeology

paper · doi:10.17323/1609-4514-2009-9-1-183-198

openalex publication_date 2009/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15

Abstract

Let Cr(k) = Autk(X; Y ) be the Cremona group of rank 2 over a eld k. We give a sharp multiplicative bound M(k) for the orders of the

Citations

• Rational Curves on Algebraic Varieties
• Bounds for the orders of the finite subgroups of G(k)
• Finite Subgroups of the Plane Cremona Group

Cited by

• Automorphism groups of compact complex surfaces
• Cremona group [wikipedia]