Simple relations in the Cremona group
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- by Jérémy Blanc PDF
- Proc. Amer. Math. Soc. 140 (2012), 1495-1500 Request permission
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 $\sigma =(x:y:z)\dasharrow (yz:xz:xy)$.References
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- V. A. Iskovskikh, Proof of a theorem on relations in the two-dimensional Cremona group, Uspekhi Mat. Nauk 40 (1985), no. 5(245), 255–256 (Russian). MR 810819
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Additional Information
- Jérémy Blanc
- Affiliation: Mathematisches Institut, University of Basel, Rheinsprung 21, CH-4051 Basel, Switzerland
- MR Author ID: 744287
- Email: Jeremy.Blanc@unibas.ch
- 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
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 1495-1500
- MSC (2010): Primary 20F05, 14E07
- DOI: https://doi.org/10.1090/S0002-9939-2011-11004-9
- MathSciNet review: 2869134