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arXiv · 1303.1032

Proper triangular Ga-actions on A^4 are translations

Adrien Dubouloz·David Finston·Imad Jaradat
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Abstract

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.

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Adrien Dubouloz, David Finston, Imad Jaradat. 2013-03-05. Proper triangular Ga-actions on A^4 are translations. https://doi.org/10.2140/ant.2014.8.1959

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