Closed normal subgroups of the group of polynomial automorphisms (Jérémy Blanc, Université de Neuchâtel)

03.12.2024 10:30

The group of polynomial automorphisms of the affine plane has been studied a lot since decades. In 1942, Jung and van der Kulk proved that it is generated by affine automorphisms (linear maps and translations) and triangular automorphisms, which are automorphisms preserving one variable. It has moreover the structure of an amalgamated product over these two subgroups. The group is not simple as it contains the subgroup of automorphisms of Jacobian 1. This latter normal subgroup also contains some complicated normal subgroups, as proven by Danilov in 1974. The simplicity of this group, viewed as an infinite dimensional algebraic group, or equivalently the existence of closed normal subgroups was however often since Iskovskikh in 1966, which had produced an incomplete proof. I will give the answer to this question and explain the history and the details of the proofs.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Tuesday 3.12.2024, Séminaire "Groupes et géométrie"

entrée libre