Comptes Rendus
Algebraic Geometry
Finite Abelian subgroups of the Cremona group of the plane
[Sous-groupes abéliens finis du groupe de Cremona du plan]
Comptes Rendus. Mathématique, Volume 344 (2007) no. 1, pp. 21-26.

On présente dans cette Note quelques résultats sur les classes de conjugaisons de sous-groupes abéliens finis du groupe de Cremona du plan.

We present in this Note some results on conjugacy classes of finite Abelian subgroups of the Cremona group of the plane.

Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.11.026

Jérémy Blanc 1

1 Université de Genève, section de mathématiques, 2-4, rue du Lièvre, CP 64, 1211 Genève 4, Switzerland
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Jérémy Blanc. Finite Abelian subgroups of the Cremona group of the plane. Comptes Rendus. Mathématique, Volume 344 (2007) no. 1, pp. 21-26. doi : 10.1016/j.crma.2006.11.026. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.11.026/

[1] L. Bayle; A. Beauville Birational involutions of P2, Asian J. Math., Volume 4 (2000) no. 1, pp. 11-17

[2] A. Beauville, p-elementary subgroups of the Cremona group, J. Algebra, in press

[3] A. Beauville; J. Blanc On Cremona transformations of prime order, C. R. Acad. Sci. Paris, Ser. I, Volume 339 (2004), pp. 257-259

[4] J. Blanc http://www.unige.ch/cyberdocuments/theses2006/BlancJ/meta.html (Finite abelian subgroups of the Cremona group of the plane, Thesis, University of Geneva, 2006. Available online at)

[5] G. Castelnuovo, Sulle transformazioni cremoniane del piano, che ammettono una curva fissa, Rend. Accad. Lincei (1892); Memorie scelte, Zanichelli, Bologna (1937)

[6] T. de Fernex On planar Cremona maps of prime order, Nagoya Math. J., Volume 174 (2004)

[7] I.V. Dolgachev, V.A. Iskovskikh, Finite subgroups of the plane Cremona group, in preparation

[8] M.K. Gizatullin Defining relations for the Cremona group of the plane, Izv. Akad. Nauk SSSR Ser. Mat., Volume 46 (1982) no. 5, pp. 909-970 (1134)

[9] V.A. Iskovskikh Minimal models of rational surfaces over arbitrary fields, Izv. Akad. Nauk SSSR Ser. Mat., Volume 43 (1979) no. 1, pp. 19-43 (237)

[10] V.A. Iskovskikh Generators and relations in a two-dimensional Cremona group, Vestnik Moskov. Univ. Ser. I Mat. Mekh., Volume 5 (1983) no. 310, pp. 43-48

[11] V.A. Iskovskikh Factorization of birational mappings of rational surfaces from the point of view of Mori theory, Uspekhi Mat. Nauk, Volume 51 4 (1996) no. 310, pp. 3-72

[12] S. Kantor Theorie der endlichen Gruppen von eindeutigen Transformationen in der Ebene, Mayer & Müller, Berlin, 1895

[13] Yu. Manin Rational surfaces over perfect fields, II, Math. USSR-Sb., Volume 1 (1967), pp. 141-168

[14] A. Wiman Zur Theorie der endlichen Gruppen von birationalen Transformationen in der Ebene, Math. Ann., Volume 48 (1896), pp. 497-498 (195–241)

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