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Article Dans Une Revue International Journal of Mathematics Année : 2016

Rationally integrable vector fields and rational additive group actions

Résumé

We characterize rational actions of the additive group on algebraic varieties defined over a field of characteristic zero in terms of a suitable integrability property of their associated velocity vector fields. This extends the classical correspondence between regular actions of the additive group on affine algebraic varieties and the so-called locally nilpotent derivations of their coordinate rings. Our results lead in particular to a complete characterization of regular additive group actions on semi-affine varieties in terms of their associated vector fields. Among other applications, we review properties of the rational counterpart of the Makar-Limanov invariant for affine varieties and describe the structure of rational homogeneous additive group actions on toric varieties.
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Dates et versions

hal-01407992 , version 1 (02-12-2016)

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Adrien Dubouloz, Alvaro Liendo. Rationally integrable vector fields and rational additive group actions. International Journal of Mathematics, 2016, 27 (8), ⟨10.1142/S0129167X16500609⟩. ⟨hal-01407992⟩
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