Simple relations in the Cremona group

Jérémy Blanc
2012 Proceedings of the American Mathematical Society  
We give a simple set of generators and relations for the Cremona group of the plane. Namely, we show that the Cremona group is the amalgamated product of the de Jonqui\'eres group with the group of automorphisms of the plane, divided by one relation which is $\sigma\tau=\tau\sigma$, where $\tau=(x:y:z)\mapsto (y:x:z)$ and $\sigma=(x:y:z)\dasharrow (yz:xz:xy)$.
doi:10.1090/s0002-9939-2011-11004-9 fatcat:cr6ggiidrzeztl7qlsylbbtisq