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arXiv · 1011.4432

Simple relations in the Cremona group

Jérémy Blanc
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Abstract

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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Jérémy Blanc. 2010-11-19. Simple relations in the Cremona group. https://doi.org/10.1090/s0002-9939-2011-11004-9

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