Le groupe de Cremona est connexe en toute dimension et, muni de sa topologie, il est simple en dimension
The Cremona group is connected in any dimension and, endowed with its topology, it is simple in dimension
Mot clés : groupe de Cremona, topologie, connexité, simplicité
Keywords: Cremona group, topology, connectivity, simplicity
@article{ASENS_2010_4_43_2_357_0, author = {Blanc, J\'er\'emy}, title = {Groupes de {Cremona,} connexit\'e et simplicit\'e}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {357--364}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {4e s{\'e}rie, 43}, number = {2}, year = {2010}, doi = {10.24033/asens.2123}, mrnumber = {2662668}, zbl = {1193.14017}, language = {fr}, url = {https://www.numdam.org/articles/10.24033/asens.2123/} }
TY - JOUR AU - Blanc, Jérémy TI - Groupes de Cremona, connexité et simplicité JO - Annales scientifiques de l'École Normale Supérieure PY - 2010 SP - 357 EP - 364 VL - 43 IS - 2 PB - Société mathématique de France UR - https://www.numdam.org/articles/10.24033/asens.2123/ DO - 10.24033/asens.2123 LA - fr ID - ASENS_2010_4_43_2_357_0 ER -
%0 Journal Article %A Blanc, Jérémy %T Groupes de Cremona, connexité et simplicité %J Annales scientifiques de l'École Normale Supérieure %D 2010 %P 357-364 %V 43 %N 2 %I Société mathématique de France %U https://www.numdam.org/articles/10.24033/asens.2123/ %R 10.24033/asens.2123 %G fr %F ASENS_2010_4_43_2_357_0
Blanc, Jérémy. Groupes de Cremona, connexité et simplicité. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 43 (2010) no. 2, pp. 357-364. doi : 10.24033/asens.2123. https://www.numdam.org/articles/10.24033/asens.2123/
[1] Non-simplicity of the group of unimodular automorphisms of an affine plane, Mat. Zametki 15 (1974), 289-293. | MR | Zbl
,[2] Sous-groupes algébriques de rang maximum du groupe de Cremona, Ann. Sci. École Norm. Sup. 3 (1970), 507-588. | Numdam | MR | Zbl
,[3] La géométrie des groupes classiques, Ergebn. der Math. und ihrer Grenzg. 5, Springer, 1971. | MR | Zbl
,[4] 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. | MR | Zbl
,[5] 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. | Zbl
,[6] Une remarque sur la génération du groupe de Cremona, Bol. Soc. Brasil. Mat. (N.S.) 30 (1999), 95-98. | MR | Zbl
,[7] Communication personnelle.
,[8] Le groupe de Cremona et ses sous-groupes finis, Séminaire Bourbaki, vol. 2008/09, exposé no 1000, à paraître dans Astérisque. | Numdam | Zbl
,[9] Algebraic surfaces, Proc. Steklov Inst. Math. 75, 1967. | Zbl
,- Geometry on Surfaces, a Source for Mathematical Developments, Surveys in Geometry II (2024), p. 7 | DOI:10.1007/978-3-031-43510-2_2
- Bijective Cremona transformations of the plane, Selecta Mathematica, Volume 28 (2022) no. 3 | DOI:10.1007/s00029-022-00768-0
- Three plots about the Cremona groups, Izvestiya: Mathematics, Volume 83 (2019) no. 4, p. 830 | DOI:10.1070/im8831
- Три сюжета о группах Кремоны, Известия Российской академии наук. Серия математическая, Volume 83 (2019) no. 4, p. 194 | DOI:10.4213/im8831
- Геометрия вербальных уравнений в простых алгебраических группах над специальными полями, Успехи математических наук, Volume 73 (2018) no. 5(443), p. 3 | DOI:10.4213/rm9838
- Borel subgroups of Cremona groups, Mathematical Notes, Volume 102 (2017) no. 1-2, p. 60 | DOI:10.1134/s0001434617070070
- Борелевские подгруппы групп Кремоны, Математические заметки, Volume 102 (2017) no. 1, p. 72 | DOI:10.4213/mzm11562
- Dixmier groups and Borel subgroups, Advances in Mathematics, Volume 286 (2016), p. 387 | DOI:10.1016/j.aim.2015.09.012
- Conjugacy classes of special automorphisms of the affine spaces, Algebra Number Theory, Volume 10 (2016) no. 5, p. 939 | DOI:10.2140/ant.2016.10.939
- On degenerations of plane Cremona transformations, Mathematische Zeitschrift, Volume 282 (2016) no. 1-2, p. 223 | DOI:10.1007/s00209-015-1539-z
- A connection between birational automorphisms of the plane and linear systems of curves, Journal of Computational and Applied Mathematics, Volume 283 (2015), p. 91 | DOI:10.1016/j.cam.2015.01.026
- Some properties of the group of birational maps generated by the automorphisms of
P C n and the standard involution, Mathematische Zeitschrift, Volume 281 (2015) no. 3-4, p. 893 | DOI:10.1007/s00209-015-1512-x - Normal subgroups in the Cremona group, Acta Mathematica, Volume 210 (2013) no. 1, p. 31 | DOI:10.1007/s11511-013-0090-1
- Topologies and structures of the Cremona groups, Annals of Mathematics, Volume 178 (2013) no. 3, p. 1173 | DOI:10.4007/annals.2013.178.3.8
- Tori in the Cremona groups, Izvestiya: Mathematics, Volume 77 (2013) no. 4, p. 742 | DOI:10.1070/im2013v077n04abeh002659
- Торы в группах Кремоны, Известия Российской академии наук. Серия математическая, Volume 77 (2013) no. 4, p. 103 | DOI:10.4213/im8021
- Normal subgroup generated by a plane polynomial automorphism, Transformation Groups, Volume 15 (2010) no. 3, p. 577 | DOI:10.1007/s00031-010-9095-4
Cité par 17 documents. Sources : Crossref