Sur les automorphismes du groupe de Cremona

Julie Déserti

doi:10.1112/S0010437X06002478

Abstract

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We prove that an automorphism of the group of birational transformations of the complex projective plane is the composition of an interior automorphism and an automorphism of the field $\mathbb{C}$. The proof is based on a study of maximal abelian subgroups of the Cremona group.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Déserti, Julie 2009. Quelques propriétés des transformations birationnelles du plan projectif complexe, une histoire pour S.. Séminaire de théorie spectrale et géométrie, Vol. 27, Issue. , p. 45.

Cantat, Serge 2011. Sur les groupes de transformations birationnelles des surfaces. Annals of Mathematics, Vol. 174, Issue. 1, p. 299.

Kunyavskiĭ, Boris 2013. Local–global invariants of finite and infinite groups: Around Burnside from another side. Expositiones Mathematicae, Vol. 31, Issue. 3, p. 256.

Cantat, Serge Lamy, Stéphane and Cornulier, Yves 2013. Normal subgroups in the Cremona group. Acta Mathematica, Vol. 210, Issue. 1, p. 31.

Cantat, Serge 2014. Morphisms between Cremona groups, and characterization of rational varieties. Compositio Mathematica, Vol. 150, Issue. 7, p. 1107.

Déserti, Julie 2015. On solvable subgroups of the Cremona group. Illinois Journal of Mathematics, Vol. 59, Issue. 2,

Déserti, Julie 2015. Some properties of the group of birational maps generated by the automorphisms of $${\mathbb {P}}^n_{\mathbb {C}}$$ P C n and the standard involution. Mathematische Zeitschrift, Vol. 281, Issue. 3-4, p. 893.

Martin, Alexandre 2017. On the acylindrical hyperbolicity of the tame automorphism group of SL2(C). Bulletin of the London Mathematical Society, Vol. 49, Issue. 5, p. 881.

CERVEAU, Dominique and DÉSERTI, Julie 2018. Birational maps preserving the contact structure on $\mathbb{P}^3_\mathbb{C}$. Journal of the Mathematical Society of Japan, Vol. 70, Issue. 2,

Urech, Christian and Zimmermann, Susanna 2021. Continuous automorphisms of Cremona groups. International Journal of Mathematics, Vol. 32, Issue. 04, p. 2150019.

Zikas, Sokratis 2023. Rigid birational involutions of ℙ 3 and cubic threefolds. Journal de l’École polytechnique — Mathématiques, Vol. 10, Issue. , p. 233.

Article contents

Sur les automorphismes du groupe de Cremona

Abstract

Keywords

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

Sur les automorphismes du groupe de Cremona

Abstract

Keywords

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