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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Simple relations in the Cremona group


Author: Jérémy Blanc
Journal: Proc. Amer. Math. Soc. 140 (2012), 1495-1500
MSC (2010): Primary 20F05, 14E07
Published electronically: August 18, 2011
MathSciNet review: 2869134
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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 Jonquières 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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Additional Information

Jérémy Blanc
Affiliation: Mathematisches Institut, University of Basel, Rheinsprung 21, CH-4051 Basel, Switzerland
Email: Jeremy.Blanc@unibas.ch

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11004-9
PII: S 0002-9939(2011)11004-9
Received by editor(s): October 29, 2010
Received by editor(s) in revised form: January 11, 2011
Published electronically: August 18, 2011
Additional Notes: This work was supported by SNSF grant No. PP00P2_128422/1
Communicated by: Ken Ono
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.