6533b826fe1ef96bd1285282

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Proper triangular Ga-actions on A^4 are translations

Adrien DuboulozImad JaradatDavid R. Finston

subject

Algebraaffine spacesMathematics - Algebraic GeometryAlgebra and Number Theorygeometric quotientFOS: Mathematics14L30; 14R20; 14R25[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]Algebraic Geometry (math.AG)proper additive group actionsMathematics[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]

description

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.

yearjournalcountryeditionlanguage
2013-03-05
10.2140/ant.2014.8.1959http://arxiv.org/abs/1303.1032