Cremona group, connectedness and simplicity

Jérémy Blanc

Annales scientifiques de l'École Normale Supérieure (2010)

  • Volume: 43, Issue: 2, page 357-364
  • ISSN: 0012-9593

Abstract

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The Cremona group is connected in any dimension and, endowed with its topology, it is simple in dimension 2 .

How to cite

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Blanc, Jérémy. "Groupes de Cremona, connexité et simplicité." Annales scientifiques de l'École Normale Supérieure 43.2 (2010): 357-364. <http://eudml.org/doc/272247>.

@article{Blanc2010,
abstract = {Le groupe de Cremona est connexe en toute dimension et, muni de sa topologie, il est simple en dimension $2$.},
author = {Blanc, Jérémy},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Cremona group; topology; connectivity; simplicity},
language = {fre},
number = {2},
pages = {357-364},
publisher = {Société mathématique de France},
title = {Groupes de Cremona, connexité et simplicité},
url = {http://eudml.org/doc/272247},
volume = {43},
year = {2010},
}

TY - JOUR
AU - Blanc, Jérémy
TI - Groupes de Cremona, connexité et simplicité
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2010
PB - Société mathématique de France
VL - 43
IS - 2
SP - 357
EP - 364
AB - Le groupe de Cremona est connexe en toute dimension et, muni de sa topologie, il est simple en dimension $2$.
LA - fre
KW - Cremona group; topology; connectivity; simplicity
UR - http://eudml.org/doc/272247
ER -

References

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  1. [1] V. I. Danilov, Non-simplicity of the group of unimodular automorphisms of an affine plane, Mat. Zametki15 (1974), 289–293. Zbl0309.12104MR357626
  2. [2] M. Demazure, Sous-groupes algébriques de rang maximum du groupe de Cremona, Ann. Sci. École Norm. Sup.3 (1970), 507–588. Zbl0223.14009MR284446
  3. [3] J. A. Dieudonné, La géométrie des groupes classiques, Ergebn. der Math. und ihrer Grenzg. 5, Springer, 1971. Zbl0221.20056MR310083
  4. [4] M. H. Gizatullin, The decomposition, inertia and ramification groups in birational geometry, in Algebraic geometry and its applications (Yaroslavlʼ, 1992), Aspects Math. E 25, Vieweg, 1994, 39–45. Zbl0834.14006MR1282018
  5. [5] D. Mumford, Algebraic geometry, in Mathematical developments arising from Hilbert problems. Proceedings of the Symposium in Pure Mathematics of the American Mathematical Society held at Northern Illinois University, De Kalb, 1974, 44–45. Zbl0326.00002
  6. [6] I. Pan, Une remarque sur la génération du groupe de Cremona, Bol. Soc. Brasil. Mat. (N.S.) 30 (1999), 95–98. Zbl0972.14006MR1686984
  7. [7] J-P. Serre, Communication personnelle. 
  8. [8] J-P. Serre, Le groupe de Cremona et ses sous-groupes finis, Séminaire Bourbaki, vol. 2008/09, exposé no 1000, à paraître dans Astérisque. Zbl1257.14012
  9. [9] I. R. Shafarevich, Algebraic surfaces, Proc. Steklov Inst. Math. 75, 1967. Zbl0832.14026

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