On rational additive group actions

Abstract : 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. This leads 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 counter-part 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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Submitted on : Saturday, September 20, 2014 - 12:12:39 AM
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  • HAL Id : hal-01066426, version 1
  • ARXIV : 1409.5878

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Adrien Dubouloz, Alvaro Liendo. On rational additive group actions. 2014. ⟨hal-01066426⟩

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