Proper triangular Ga-actions on A^4 are translations

Adrien Dubouloz (1) , David Finston (2) , Imad Jaradat (3)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 Mathematics Department
3 Department of Mathematical Sciences

We describe the structure of geometric quotients for proper locally triangulable additve group actions on locally trivial A^3-bundles over a noetherian normal base scheme X defined over a field of characteristic 0. In the case where dim X=1, we show in particular that every such action is a translation with geometric quotient isomorphic to the total space of a vector bundle of rank 2 over X. As a consequence, every proper triangulable Ga-action on the affine four space A^4 over a field of characteristic 0 is a translation with geometric quotient isomorphic to A^3.

Mots clés: proper additive group actions; affine spaces; geometric quotient

Domaines: Géométrie algébrique [math.AG]

Adrien Dubouloz, David Finston, Imad Jaradat. Proper triangular Ga-actions on A^4 are translations. 2013. ⟨hal-00796972⟩