Proper triangular Ga-actions on A^4 are translations

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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Submitted on : Tuesday, March 5, 2013 - 1:50:57 PM
Last modification on : Tuesday, August 13, 2019 - 1:42:01 PM
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  • HAL Id : hal-00796972, version 1
  • ARXIV : 1303.1032

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

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