Sous-groupes alg\'ebriques du groupe de Cremona

TL;DR

This paper provides a comprehensive classification of maximal algebraic subgroups of the Cremona group of the plane and describes algebraic varieties that parametrize their conjugacy classes.

Contribution

It offers a complete classification of maximal algebraic subgroups of the Cremona group and explicitly constructs the parametrizing algebraic varieties.

Findings

Complete classification of maximal algebraic subgroups

Explicit parametrization of conjugacy classes

Identification of algebraic varieties for classification

Abstract

We give a complete classification of maximal algebraic subgroups of the Cremona group of the plane and provide algebraic varieties that parametrize the conjugacy classes. ----- Nous donnons une classification compl\`ete des sous-groupes alg\'ebriques maximaux du groupe de Cremona du plan et explicitons les vari\'et\'es qui param\`etrent les classes de conjugaison.