Simple relations in the Cremona group

Details Simple relations in the Cremona group Simple relations in the Cremona group

2010-11-19

arxiv.org/abs/1011.4432v1

Mathematics

Algebraic Geometry

Scientific paper

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 $\sigma=(x:y:z)\dasharrow (yz:xz:xy)$.

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